This is my understanding of AN4.173.
“There is not anything else” means “there is no longer something else”, which is a perfectly valid translation of na atthi aññaṁ kiñci too. So the wrong assupmtion is that something else existed outside of the six senses, but that it ceased alongside the six senses. In reality there were only the six senses, so nothing else can cease or remain.
If anything, Mahākoṭṭhita’s questions are ill phrased, because in Pāli it can mean “does something else no longer exist?”, even if it can also mean something else. And of course, Sāriputta’s reply is exactly “don’t put it like that”, which implies the wording can be taken the wrong way.
To say something else than the six senses no longer exists is also “proliferating on what should not be proliferated” (or “elaborating on what should not be elaborated”), because it goes beyond what exists—which is the six senses. If it meant “there is nothing else” it wouldn’t be proliferating (unless you take “there” as a place and “nothing” as a something).
These statements in AN4.173 are in the exact same form as those of the Tathagata after death. It is the famous tetralemma. Does the “tathagata” (i.e. self) (1) no longer exist, (2) still exist, (3) both, or (4) neither? The first amounts to annihilationism, the second is eternalism, the others are combinations of the two or just equivocation.
The commentary to AN4.173 also seems to agree that na atthi aññaṁ kiñci means annihilationism. As Bhikkhu Bodhi notes:
[The commentary] explains that the four questions are asked by way of eternalism, annihilationism, partial eternalism, and "eel-wriggling” (sassata-uccheda-ekaccasassata-amarāvikkhepa). Thus Sāriputta rejects each question. "Eel-wriggling” is agnosticism, skepticism, or intellectual evasiveness.
You are right, the aggregate of consciousness includes all consciousness whatsoever. See SN22.82 and MN109:
Whatever kind of consciousness there is—whether past, future, or present, internal or external, gross or subtle, inferior or superior, far or near—this is called the consciousness aggregate.
The sutta also says it called an “aggregates” because it “aggregates” (or includes) all consciousness.