conditionals - Use of "may" or "might" and their inherent semantic difference

Under the American Heritage Dictionary's usage note for the verb "might" it says:

Usage Note: May or might? In many situations, the choice between these two verbs can be clarified by remembering that might is the past tense form of may, and that in English, a past tense form is used to refer not just to events that occurred in the past (She left yesterday), but to hypothetical, counterfactual, or remotely possible situations (If you left now, you'd get there on time.)

It's emphasizing that in the following:

If you left now, you'd get there on time.

We use the past tense "left" for a hypothetical, counterfactual, or remotely possible situation.

If I don't use the past tense "left" and instead use the present tense:

If you leave now, you'd get there on time.

I feel that this has the same meaning. Am I wrong?

Further:

Thus, the past tense form might is appropriate in this sentence about a future event that is a remote possibility: ‘If I won the lottery, I might buy a yacht’, which contrasts with the present-tense version that indicates an open possibility: ‘If I win the lottery, I may buy a yacht’.

The first example it describes as a "remote possibility", and the second is described as an "open possibility". Is this implying that "might" is used when there is a lower likelihood in the conditional statement? In the following examples:

• If I won the lottery, I might buy a yacht.
  


• If I won the lottery, I may buy a yacht.
  


• If I win the lottery, I might buy a yacht.
  


• If I win the lottery, I may buy a yacht.
  

I struggle to see a significant difference in their meanings, if any at all. All of them mean to me something like:

• If in the future I win the lottery, I may/might by a yacht.

I don't consciously see any difference between "remote possibility" or "open possibility", or any distinction in probability. Am I wrong?

It then explains that when using "might" and "may" to denote past counter-factual or conditional situations their usage panel generally disapproves of "may" and favors "might":

Since about the 1960s, however, people have started using may have where might have would be expected (as in, ‘If he hadn't tripped, he may have won the race’). Although this usage is common in casual speech, it is considered unacceptable by the majority of the Usage Panel. In our 2012 survey, 97 percent of the Usage Panelists found the sentence ‘If John Lennon had not been shot, the Beatles might have gotten back together’ acceptable. Only a third of the Panel (32 percent) approved of the same sentence with may have replacing might have.

So I understand its disapproval by their usage panel. Next, it says another thing that I also don't understand:

Using may have for a past counterfactual situation instead of might have is not only frowned upon by the Panel but can also lead to confusion, since may have is best suited for a different kind of situation: present uncertainty about a past situation. Keeping the two forms distinct reduces ambiguity. ‘He may have drowned’, for example, is best used to mean that it is unknown whether the man drowned, not that the man narrowly escaped drowning.

Again, as far as I can tell both:

• He may have drowned.
  or
  


• He might have drowned.
  

In my opinion, could be read as:

• He may have drowned, he may be dead.
  or
  


• He might have drowned, he may be dead.
  or
  


• He may have drowned, he's lucky to be alive.
  or
  


• He might have drowned, he's lucky to be alive.
  

The very last sentence I would say is probably one where "might" sounds a bit strange, and "may" fits better. But the main point is that using "may" or "might" in the bare sentence:

• He may/might have drowned.
  

To me doesn't necessarily distinguish between two meanings, nor do I think it suggests it (by itself at least).

Later in the explanation, it says that it's actually been suggested that "might" carries a lesser probability than "may", but I don't personally see this, at least in the examples I've seen.

So how wrong am I? I'm completely blind to nearly all of the distinctions drawn in the dictionary's usage note. Is it that I don't understand the real nuances, or is it that largely they've become interchangeable (a point it also mentioned in the usage notes).

When may and might are used to indicate possibility or probability, as in ‘He may lose his job’ or ‘We might go on vacation next year’, the two words are used almost interchangeably.

Addition:

It seems some (no idea what proportion) make the distinction between might to mean "might have happened (but we don't know) vs may to mean "may have happened (but didn't). This has been mentioned by at least one user who personally makes the distinction themself. I've checked Random House Kernerman Webster's College Dictionary and the entries are:

2.(used to express tentative possibility):
She might have called while you were out.
3.(used to express an unrealized possibility):
He might have been killed!

(2) is described as "tentative possibility", that is, "she might have called while you were out (but we don't know)", and (3) is described as "unrealized possibility", that is, "He might have been killed! (but wasn't)". It does distinguish between what it calls "tentative possibility" and "unrealized possibility", much as AHD's usage note does. If I understand correctly dictionaries usually list their definitions from most to least common, so it's interesting that it hasn't listed them in the opposite order: (3) and (2). I think this is a distinction I've just lost, or never had in the first place. However I like distinctions in words wherever they may be, so I'm happy to learn this and put it into practice, while of course not being a pedant and insisting that it's the "correct" usage of might and may. I'd also like to know if others make this distinction. Maybe you can let me know through a comment.