I am not sure this reading can be sustained. First of all it appears that SN44.10 is a very short precis of the much more detailed and substantive MN72. Second the siding with eternalists or with annihilationists is given a much more philosophically nuanced gloss in SN12.17 that doesn’t seem to have the same opportunity to declare the subject under question a fiction.
There we have:
“Well, Master Gotama, is suffering made by oneself?”
“Kiṁ nu kho, bho gotama, ‘sayaṅkataṁ dukkhan’ti?“Not so, Kassapa,” said the Buddha.
‘Mā hevaṁ, kassapā’ti bhagavā avoca.“Then is suffering made by another?”
‘Kiṁ pana, bho gotama, paraṅkataṁ dukkhan’ti?“Not so, Kassapa,” said the Buddha.
‘Mā hevaṁ, kassapā’ti bhagavā avoca.“Well, is suffering made by both oneself and another?”
‘Kiṁ nu kho, bho gotama, sayaṅkatañca paraṅkatañca dukkhan’ti?“Not so, Kassapa,” said the Buddha.
‘Mā hevaṁ, kassapā’ti bhagavā avoca.“Then does suffering arise by chance, not made by oneself or another?”
‘Kiṁ pana, bho gotama, asayaṅkāraṁ aparaṅkāraṁ adhiccasamuppannaṁ dukkhan’ti?“Not so, Kassapa,” said the Buddha.
‘Mā hevaṁ, kassapā’ti bhagavā avoca.“Well, is there no such thing as suffering?”
‘Kiṁ nu kho, bho gotama, natthi dukkhan’ti?“It’s not that there’s no such thing as suffering.
‘Na kho, kassapa, natthi dukkhaṁ.Suffering is real.”
Atthi kho, kassapa, dukkhan’ti.
This obviously does not directly bear on the ontological status of an ‘atta’, but it does make it difficult to maintain that where we see the Buddha denying the 4 alternatives (as at MN72) he is doing so because of a fictionalism with regard to the subject under scrutiny, as here the subject is suffering, and it is explicitly asserted as “real”
later in the same sutta, the Buddha says of his reasoning:
“Suppose that the person who does the deed experiences the result. Then for one who has existed since the beginning, suffering is made by oneself. This statement leans toward eternalism.
“‘So karoti so paṭisaṁvedayatī’ti kho, kassapa, ādito sato ‘sayaṅkataṁ dukkhan’ti iti vadaṁ sassataṁ etaṁ pareti.Suppose that one person does the deed and another experiences the result. Then for one stricken by feeling, suffering is made by another. This statement leans toward annihilationism.
‘Añño karoti añño paṭisaṁvedayatī’ti kho, kassapa, vedanābhitunnassa sato ‘paraṅkataṁ dukkhan’ti iti vadaṁ ucchedaṁ etaṁ pareti.Avoiding these two extremes, the Realized One teaches by the middle way:
Ete te, kassapa, ubho ante anupagamma majjhena tathāgato dhammaṁ deseti:‘Ignorance is a condition for choices.
‘avijjāpaccayā saṅkhārā;
Here again, it is difficult to see how we can make sense of this on the fictionalist account, for then we should, at worst, have the third option, “Then does suffering arise by chance, not made by oneself or another?” and at best we should have a clear statement like “there is no such thing as a self” (since we have the clear denial of such a statement with regard to suffering it seems that the linguistic resource was available to the Buddha).
Furthur we have the “leaning toward” explanation that seems to indicate that the problem with the annihilation position isn’t simply with the idea of a real but temporary self, but with the incoherence of one such temporary self being the cause of the affliction of another, later and therefore different temporary self. Again, this is a different reason than “persons are fictions” which, again, it is clearly open to the Buddha to say if that is what he thinks.
I would also note that this is the reasoning given first in SN44.10 and that the second set of reasons given (the sabbe dhamma anatta reason and the “confusion” reason) is not reproduced here.
I am not sure this is true, I have listed every appearance of Vacchagotta in the canon here
And it appears to me that there are really only 2 substantive exchanges, and there seems a good chance that really there is just one incident being described, anyway, in the much more substantial MN72 we get the fire simile relating again to a slightly different question to the atta question, about the status of the enlightened one after death:
“But Master Gotama, when a mendicant’s mind is freed like this, where are they reborn?”
“Evaṁ vimuttacitto pana, bho gotama, bhikkhu kuhiṁ upapajjatī”ti?
“‘They’re reborn’ doesn’t apply, Vaccha.”
“Upapajjatīti kho, vaccha, na upeti”.
“Well then, are they not reborn?”
“Tena hi, bho gotama, na upapajjatī”ti?
“‘They’re not reborn’ doesn’t apply, Vaccha.”
“Na upapajjatīti kho, vaccha, na upeti”.
“Well then, are they both reborn and not reborn?”
“Tena hi, bho gotama, upapajjati ca na ca upapajjatī”ti?
“‘They’re both reborn and not reborn’ doesn’t apply, Vaccha.”
“Upapajjati ca na ca upapajjatīti kho, vaccha, na upeti”.
“Well then, are they neither reborn nor not reborn?”
“Tena hi, bho gotama, neva upapajjati na na upapajjatī”ti?
“‘They’re neither reborn nor not reborn’ doesn’t apply, Vaccha.”
“Neva upapajjati na na upapajjatīti kho, vaccha, na upeti”.
“Master Gotama, when asked all these questions, you say: ‘It doesn’t apply.’
“‘Evaṁ vimuttacitto pana, bho gotama, bhikkhu kuhiṁ upapajjatī’ti iti puṭṭho samāno ‘upapajjatīti kho, vaccha, na upetī’ti vadesi. ‘Tena hi, bho gotama, na upapajjatī’ti iti puṭṭho samāno ‘na upapajjatīti kho, vaccha, na upetī’ti vadesi. ‘Tena hi, bho gotama, upapajjati ca na ca upapajjatī’ti iti puṭṭho samāno ‘upapajjati ca na ca upapajjatīti kho, vaccha, na upetī’ti vadesi. ‘Tena hi, bho gotama, neva upapajjati na na upapajjatī’ti iti puṭṭho samāno ‘neva upapajjati na na upapajjatīti kho, vaccha, na upetī’ti vadesi.
I fail to understand this point, Master Gotama; I’ve fallen into confusion.
Etthāhaṁ, bho gotama, aññāṇamāpādiṁ, ettha sammohamāpādiṁ.
And I’ve now lost even the degree of clarity I had from previous discussions with Master Gotama.”
Yāpi me esā bhoto gotamassa purimena kathāsallāpena ahu pasādamattā sāpi me etarahi antarahitā”ti.
“No wonder you don’t understand, Vaccha, no wonder you’re confused.
“Alañhi te, vaccha, aññāṇāya, alaṁ sammohāya.
For this principle is deep, hard to see, hard to understand, peaceful, sublime, beyond the scope of logic, subtle, comprehensible to the astute.
Gambhīro hāyaṁ, vaccha, dhammo duddaso duranubodho santo paṇīto atakkāvacaro nipuṇo paṇḍitavedanīyo.
It’s hard for you to understand, since you have a different view, creed, preference, practice, and tradition.
So tayā dujjāno aññadiṭṭhikena aññakhantikena aññarucikena aññatrayogena aññatrācariyakena.
Well then, Vaccha, I’ll ask you about this in return, and you can answer as you like.
Tena hi, vaccha, taññevettha paṭipucchissāmi; yathā te khameyya tathā naṁ byākareyyāsi.
What do you think, Vaccha?
Taṁ kiṁ maññasi, vaccha,
Suppose a fire was burning in front of you. Would you know:
sace te purato aggi jaleyya, jāneyyāsi tvaṁ:
‘This fire is burning in front of me’?”
‘ayaṁ me purato aggi jalatī’”ti?
“Yes, I would, Master Gotama.”
“Sace me, bho gotama, purato aggi jaleyya, jāneyyāhaṁ: ‘ayaṁ me purato aggi jalatī’”ti.
“But Vaccha, suppose they were to ask you:
“Sace pana taṁ, vaccha, evaṁ puccheyya: ‘
This fire burning in front of you: what does it depend on to burn?’ How would you answer?”
‘yo te ayaṁ purato aggi jalati ayaṁ aggi kiṁ paṭicca jalatī’ti, evaṁ puṭṭho tvaṁ, vaccha, kinti byākareyyāsī”ti?
“Sace maṁ, bho gotama, evaṁ puccheyya:
“I would answer like this:
‘yo te ayaṁ purato aggi jalati ayaṁ aggi kiṁ paṭicca jalatī’ti, evaṁ puṭṭho ahaṁ, bho gotama, evaṁ byākareyyaṁ:
‘This fire burning in front of me burns in dependence on grass and logs as fuel.’”
‘yo me ayaṁ purato aggi jalati ayaṁ aggi tiṇakaṭṭhupādānaṁ paṭicca jalatī’”ti.
“Suppose that fire burning in front of you was extinguished. Would you know:
“Sace te, vaccha, purato so aggi nibbāyeyya, jāneyyāsi tvaṁ:
‘This fire in front of me is extinguished’?”
‘ayaṁ me purato aggi nibbuto’”ti?
“Yes, I would, Master Gotama.”
“Sace me, bho gotama, purato so aggi nibbāyeyya, jāneyyāhaṁ: ‘ayaṁ me purato aggi nibbuto’”ti.
“But Vaccha, suppose they were to ask you:
“Sace pana taṁ, vaccha, evaṁ puccheyya:
‘This fire in front of you that is extinguished: in what direction did it go—
‘yo te ayaṁ purato aggi nibbuto so aggi ito katamaṁ disaṁ gato—
east, south, west, or north?’ How would you answer?”
puratthimaṁ vā dakkhiṇaṁ vā pacchimaṁ vā uttaraṁ vā’ti, evaṁ puṭṭho tvaṁ, vaccha, kinti byākareyyāsī”ti?
“It doesn’t apply, Master Gotama. The fire depended on grass and logs as fuel. When that runs out, and no more fuel is added, the fire is reckoned to have become extinguished due to lack of fuel.”
“Na upeti, bho gotama, yañhi so, bho gotama, aggi tiṇakaṭṭhupādānaṁ paṭicca ajali tassa ca pariyādānā aññassa ca anupahārā anāhāro nibbutotveva saṅkhyaṁ gacchatī”ti. Variant: ajali → jalati (sya-all, km, mr)
“In the same way, Vaccha, any form by which a Realized One might be described has been cut off at the root, made like a palm stump, obliterated, and unable to arise in the future.
“Evameva kho, vaccha, yena rūpena tathāgataṁ paññāpayamāno paññāpeyya taṁ rūpaṁ tathāgatassa pahīnaṁ ucchinnamūlaṁ tālāvatthukataṁ anabhāvaṅkataṁ āyatiṁ anuppādadhammaṁ.
A Realized One is freed from reckoning in terms of form. They’re deep, immeasurable, and hard to fathom,
Rūpasaṅkhayavimutto kho, vaccha, tathāgato gambhīro appameyyo duppariyogāḷho— like the ocean. seyyathāpi mahāsamuddo.
‘They’re reborn’, ‘they’re not reborn’, ‘they’re both reborn and not reborn’, ‘they’re neither reborn nor not reborn’—none of these apply.
Upapajjatīti na upeti, na upapajjatīti na upeti, upapajjati ca na ca upapajjatīti na upeti, neva upapajjati na na upapajjatīti na upeti.
Again, here the fictionalist account seems to struggle, the fire in the analogy, like the suffering in SN12.17 is real, not fictional fire, and the inappropriateness of applying cardinal directions to its status after extinguishment is a categorical error, not an error of applying a term to a fictional entity.
Of course it may be that in the case of the status of suffering and the status of the enlightened after death there is a one philosophy being invoked , while in the atta case there is a different position.
It would certainly be more intellectually satisfying in my opinion if it turned out that all cases where examples of a consistent philosophical argument that worked the same way in each case.
For another example at DN29 we get:
Pleasure and pain are eternal,
‘Sassataṁ sukhadukkhaṁ …or not eternal,
asassataṁ sukhadukkhaṁ …or both eternal and not eternal,
sassatañca asassatañca sukhadukkhaṁ …or neither eternal nor not eternal.
nevasassataṁ nāsassataṁ sukhadukkhaṁ …
Now again, this seems to be the same structure as before, and there seems to be no implication that pleasure and pain are fictitious, rather that any way of thinking about them in terms that make them substantive or fictitious makes them in some sense inescapable…
Anyhoo, all this is to say that while think the idea that not-self is a “strategy” is silly, I also think that the idea that persons are fictions is sort of silly and I think that there is plenty in the EBT’s that could be used to defend a the notion that Buddha was a metaphysical quietest with relation to views of BOTH the form “a self exists” and the form “no self exists”. (and both and neither)
This is a first draft of this response and I reserve the right to substantively revise it should my understanding change 
Metta.