I previously deleted the earlier thread for seeing it turned into a sad flaming ordeal, but Bhante @Sunyo was gracious enough to type a reply to me in PM, and with his blessings I’m sharing his insightful reply:
Thanks @Dogen, for bringing this up.
I wasn’t aware Ven. @Sujato changed his translation of the Yamaka Sutta. However, I am not convinced we’re dealing with a “label use of the nominative”, as the venerable notes. It seems to me that ti goes with the verb samanupassati to indicate how things are regarded. Essentially, it indicates a thought, which is a standard use of ti.
The Pali manuscripts differ a bit, but let’s take the CST4 (Burmese) version:
vedanaṃ ‘tathāgato’ti samanupassasi? (SN22.85)
Ven Sujato translates this as “do you consider that the label ‘realized one’ applies to feeling?” But we can compare it to:
vedanaṃ ‘etaṃ mama, esohamasmi, eso me attā’ti samanupassati (e.g. MN22)
We wouldn’t translate this as something like “he considers that the label ‘this is mine etc’ applies to feeling”. Instead, the idea is that “he regards feeling as ‘this is mine etc’”. Similarly for the Yamaka Sutta.
Ven Sujato’s old translation seems better: “Do you regard the Realized One as feeling?” Ven Bodhi translates similarly, but I think rightly turns the two words around: “Do you regard feeling as the Tathāgata?” I have: “Do you regard feeling to be a Truthfinder?” which means the same but I think is a bit clearer. It also aligns with the parallel at SA104, where the Buddha just asks: “Is feeling the Tathāgata?”
The Yamaka Sutta also mentions other relations between the aggragates and the Tathāgata. But I think these should be translated in similar ways.
Now, on your three options of interpreting these matters, @Dogen.
You quoted Ven. Ñanavira, who argues that
the reason why the Tathāgata is not to be found (even here and now) is that he is […] free from reckoning as [the aggregates]. This is precisely not the case with the puthujjana, who, in this sense, actually and in truth is to be found. (Clearing the Path, p44)
But this is not how the Yamaka Sutta itself explains the matter. The reason is not that the Tathāgata himself is free from reckoning as/identifying with the aggregates. The Tathāgata is not “to be found” by Yamaka (or whatever third person) because it’s Yamaka who is free from identifying a Tathāgata. And if Yamaka (or whoever) is free from such identifying, then they won’t identify anybody as an entity, including the putthujjanas.
We can also ask, how could Yamaka know whether other people are enlightened or not? If he knows, then how? And if he doesn’t know, how would he still “find” a putthujana but not a Tathāgata?
Ñanavira further states
the question [in MN22] whether saccato thetato [“actually and truly”] a ‘self’ is to be found, must be kept clearly distinct from another question [in SN22.85–86] whether saccato thetato the Tathāgata (or an arahat) is to be found.
But this is difficult to uphold, considering the similar context of anattā and the unique, near-identical wording in both cases. Further, the four notions about a Tathāgata after death arise from taking the aggregates as a self. (SN44.8) Just like any view of self, they stem from sakkāyadiṭṭhi. (SN41.3) Also, in SN5.10 Vajirā similarly says: “there is no [inherent] being to be found”. The nonexistence of an inherent being applies to everybody, including putthujjanas.
So of your three options, I think the third applies: the question about the Tathāgata is essentially the same as that about the self.
But you’re right: the question then arises why the matter is usually phrased in terms of the enlightened beings (tathāgatas) and not beings in general. I’m not sure. Perhaps it is incidental, indeed.
Or perhaps questions about beings in general are better answered conventionally. When asking about the rebirth (or non-rebirth) of a non-enlightened beings, it’s more pragmatic to talk about things like karma, instead of explaining that ultimately there is no real being as such.
In DN9 the Buddha even speaks about rebirth using the term attā. He then explains: “These are merely the world’s conventional labels, words, expressions, and designations, which I use without misapprehending them." Now, DN15 says that those who don’t hold the four views about the Tathāgata after death “know the extent of language and the limits of language, the extent of words and the limits of words, the extent of designations and the limits of designations”. This similarity again indicates that the four views about the Tathāgata are views of self. Both ‘self’ and ‘Tathāgata’ are just labels. We can use them conventionally, but they don’t exist as beings-in-themselves.
The Pali commentaries are aware that the term ‘Tathāgata’ refers specifically to the enlightened ones. But interestingly, they typically reframe these matters in terms of a being. However, by this they don’t mean all beings in general; they mean a being-taken-as-self, like that mentioned by Vajirā. For example, the commentary to the Yamaka Sutta clarifies that Yamaka wrongly takes ‘Tathāgata’ to be a “real, inherent being” (saccato thirato satte). Such a being “is not found to actually or really exist (saccato thetato) even while alive”, let alone after death.
The commentary further explains:
If Yamaka would have thought, ‘only produced things (saṅkhāras) arise and cease, only a process of produced things becomes nonexistent’, then it would not be a misconception but knowledge in line with the Buddha’s instructions. But because he thought, ‘a being is annihilated and destroyed’, it becomes a misconception [of annihilationism]. […]
‘What is suffering has ceased’ means that the only thing that ceased is suffering. Apart from that there is no being which ceases.
This is reminiscent of MN22, where the Buddha is accused of asserting the annihilation of a really existent being. He responds: “In the past and also now, I assert only suffering and a cessation of suffering (i.e. not the existence and annihilation of a self).” He also says this to Anurādha in SN22.86, which mentions the tetralemma on the Tathāgata after death.
About the tetralemma, the commentary to SN44.3 states:
There is just form. Apart from this form, there is not something else called a being. When there is form, there is just the name [‘Tathāgata’]. The explanation is the same for the other aggregates of feeling and so forth. The reason the Buddha does not affirm any of the propositions [about a Tathāgata after death] is that, when form and so forth are looked into, no essence (svabhāva) is obtained.
The subcommentary clarifies:
“What is rejected? The self supposed by outsiders, spoken of here [by the name] ‘Tathāgata’. The essence that is not obtained is a self.”
This is in line with the commentary to the Udāna (PTS edition):
“In ‘after death a Tathāgata still exists’, the word ‘Tathāgata’ refers to a self (attā).”
So that’s the Theravādin view. But the text of most other traditions, both early and late, also indicate in various ways that the four propositions about the Tathāgata after death all assume a self/soul. It would make for a long post to illustrate this! 
Suffice to say, this has been the default interpretation of these matters.
To me, it seems that this is in essence also the Prajnaparamita/Madhyamika interpretation. In the MMK Nāgārjuna says, in explaining the tetralemma: "How can what is without a self (anātman) be a [inherent] Tathāgata?” And Chandrakirti says:
It should be understood that all five theses [about a Tathāgata with relation to the aggregates, as in SN22.85–86] are really included in the thesis concerning identity and otherness. Nāgājuna deals with all five theses because the problem of the perfectly realized one [Tathāgata] is cognate with that of the permanent personal self. (Prasannapadā 435, translation Sprung)
