Question about μή in independent clause in Aristophanes

So, while reading Aristophanes’ the Birds (v 108), we found the following:

μῶν ἠλιαστὰ; μἀλλὰ θἀτέρου τρόπου,

There are μῶν (crasis of μὴ οὖν) and μἀλλὰ (crasis of μὴ ἀλλά). There’s a tacit νὼ ἐσμέν, implied from the previous verses (107) within the answer to the first question. LSJ does talk about one of the uses of μή: freq. without a Verb, ἄπελθε νῦν. Answ. μὴ (sc. γενέσθω) ἀλλά nay but, Aʀ. Ach. 458.
As for the first μῶν, Herbert’s Greek Grammar does talk about using μή with the indicative in questions (and with μῶν, it says that it acts similarly to Latin’s num, expecting a no-answer). But beyond that, I’m unsure why μὴ ἀλλά and not οὐκ ἀλλά.
Is it because of what LSJ’s dictionary entry mentions? Or because it’s negating the previous question with the same negative particle? And in any case, is there any explanation or just some quirks of the Greek language?

I appreciate any answer you could give me. Thanks.

Regarding μῶν, Nan Dunbar in her edition refers to Barrett’s Hippolytos comment on line 794:

Questions with μῶν (contracted from μὴ οὖν), or with μή or ἆρα μή, are often said to expect a negative answer. This, as a generalization, is quite false: I ask ‘μῶν X’ when I am reluctant to accept X as true. I may in fact, if I am convinced that X is false, expect a negative answer; but more often I at least envisage an affirmative answer – I think X is possible or even probable, and my reluctance is due to apprehension (as here), or to surprise at the possibility. The reluctance sometimes weakens down into hesitation, and the particle then may mark the question as a mere guess (e.g. Tr. 55, Ar. Ach. 418), sometimes serve as little more than a sign of interrogation (Cy. 158 is notable: Odysseus presumably both thinks X probable and approves of it). In Hipp., 974 and 1164 are apprehensive; 318 a guess tinged with apprehension; 1164 an ironical guess tinged with ironical surprise.

As for μ’ἀλλά, Dunbar writes:

μ’ἀλλά (μὴ <γένοιτο> ἀλλά) seems to be a colloquial idiom deprecating the interlocutor’s suggestion, found once or twice in Pl (Men. 75A 13, Alk I 114E1), once in Aesch. (Cho. 918), otherwise confined to Ar., cf. Ach 458-9…

Mark

I happened to drop by and just wanted to say that this is most interesting. Thanks.