Some more examples: Might as well've (well have) : "Nobody looked at the report I wrote. I might as well've not written the thing!" (I'm annoyed, frustrated, etc.) Might well've : "I can't find my keys. I might well've left them in the car." (I think maybe my keys are in the car) I'm using the contraction 'well've' because that's how I usually say it.

The use of “might as well” in this sentence is correct, to my understanding. The person is really saying; "If I don’t remember it, there was no point in it happening”. Another example: “ I tried really hard to pass my exams, but I failed them ..I might as well have not done all that hard work (i.e. there was no point in doing all the hard work, because I didn’t pass anyway) I don’t think it would be correct to use “might well” . “Might well” means to “possibly” do something..i.e. If you say this: “If I don’t remember it, it might well have not happened”. This means there is some doubt as to whether it actually happened or not. Possibly, it didn’t happen? Example of using might well: “I might well go the hairdresser next week, if I have time” (It’s possible that I’ll go to the hairdresser next week) Hope this helps!

"Might as well" is quite common. Here are some examples: We're out of milk, I might as well go to the store now. You're already in trouble, you might as well tell me what happened. It's an unusual phrase that doesn't mean literally what it says. It's a conditional that means something like "probably should" in my sentences which are the more common use. See https://idioms.thefreedictionary.com/might+as+well for more. Your sentence uses it a bit differently, more like "it's the same as if" or it "should be the same as if". "Might well" would not be a correct substitution, but it could be changed to "If I don't remember it, it's the same as if it didn't happen" or "If I don't remember it, it didn't happen". Both of those progressively lose the conditional aspect of your sentence. I can't think of another substitution that works the same way as the original.