The differende between using Perfect infinitive and past forms of may and can

Hello, thought I'm a frequent visitor of these forums, I've never felt the need of posting here before, mostly because of the fact that the solution to most of my problems has already been found here. But I haven't had luck finding solution to this particular problem yet.

The usage of the modal verbs + the perfect infinitive is well-known to me, yet there are two cases in which I don't see any differences between the meaning of the past form of the verb and the perfect infinitive construction.

These words are may and can and their past (and subjunctive) forms might and could.

I might do it. - Means that either I'll maybe do something under certain circumstances (the subjunctive form), or that I might do something referring to the past action (the past form).

I may / might have done it. - Means that I might have done something in the past. As far as I'm concerned neither of these forms expresses whether the action has been performed and both show uncertainty. I don't see any differences.

I could do it. - Means either I could do something if there was the need to do so (the subjunctive form), or that I could do something referring to the past action (the past form).

I can / could have done it. - Means that I could do something, but I didn't. I agree that this form also shows that the action wasn't performed and certain degree of regret, whilst the past form doesn't tell us whether the action was performed (Why did you kill him? Why, because I could.) The same deal with the negative form (can't / couldn't)

Yet the differences are still marginal. I'm mostly interested about the case #1 though. I should like to know whether there are ANY differences in the meaning, or if it's up to me which one of them I choose. I know that there are differences in the second case, but I might have gotten all wrong and I hope you'll correct me, should some of the information above be incorrect.

Best Regards from the Czech Republic, Witiko.