"He must have overslept, mustn't he?" versus "… , hasn't he?" or "… , didn't he?" Which is correct?

All three beg to be rephrased:

• He overslept, didn't he?
• He must have overslept, don't you think?

About 313,000 results on a Google search for "mustn't he" would perhaps indicate that people saying the usage is terrible (1) haven't checked and (2) are speaking subjectively.

UsingEnglish.com has an article addressing this debate:

He must have seen it, mustn't he?

This is the first time I have seen such a question tag as with 'must have done'. In China's English tests or examinations, such a tag is thought to be absolutely wrong. They say we must use 'hasn't he?'. They also say we must say 'He must have seen it yesterday, didn't he?'

I thought 'mustn't he?' was fine, but I had never found any proof. Now that I've got this sentence, I'd like to know how authoritative it is and whether we can use this sentence at all.

Might I ask native English teachers to help me clarify this puzzle of mine?

Joham

And after checking, as well as being familiar with the usage, I can agree with the reply [bolding mine]:

There's nothing wrong with this. Any other tag question implies an ellipsis such as 'He must have done it. [Tell me I'm not wrong. (Beginning to be unsure) He did...] Didn't he?'. In that case, it's not really a tag question at all, as it's not asking for routine confirmation of a certainty.

BobK

The modal tag-question is very common:

I can go out tonight, can't I?

They could go via Vail, couldn't they?

It would be a disaster, wouldn't it?

He must use the lift, mustn't he?

I shall die, shan't I? [formal]

He'll tell his dad, won't he?

'Mightn't' may sound a little awkward, but 'mustn't' is in regular use, at least in some areas. ODO includes the contraction and a tag-question usage:

So I thought, if it's man made, there must be someone driving it, mustn't there?

Must have done something = I am sure someone did something.

The true meaning of the sentence is the assumption that someone did do something with must have done being just a mask to it or a periphrasis. The tag question refers to the true meaning of an utterence, therefore must have done, didn't they.

However, challenging your own assumption with a tag question doesn't make much sense, therefore don't you think is the logical thing.