Hi,
As to the question of whether 'might not have had' could have been used, what would you say?
Can I say this?
Why did he not tell us the truth? He may have had a reason but we didn't hear about it at our last meeting two days ago. -- Should this be "might have had"? When do you use "might have had" and "may have had"? I really don't see any difference between 'may/might' in this kind of context, where we are discussing possibility and we don't know the outcome.
We can also speak this way with
might, to say that something was possible but did not happen. eg
You shouldn't have climbed that tree. You might have killed yourself.
You can also use this 'may/might' structure to talk about present or future.
eg I'll phone him, but he may / might have gone out by now.
eg By the end of this year, I may/might have saved enough money to buy a house.
Some of my comments and examples above are quoted from or based on looking at Michael Swan's very useful book,
Practical English Usage.Best wishes, Clive
.