Just a couple of comments on some of the points you made:
It seems that there is only one sub-mood (i.e., use) of the conditional mood -
Very few grammarians speak of a conditional mood in English.
There is a common misconception - probably brought on by poor preparation of English teachers at their School of Education, so as to make grammar not so difficult for young learners - that anything that uses "would", "could", "should", "might" is conditional.
I do not agree that this is a common misconception.
Do you have evidence of the 'poor preparation of English teachers'?
The use of "would" in a wish clause is the optative mood,
Very few grammarians speak of an optative mood in English
Also, the use of "would" for past habit is implied conditional
"Back in the day, I would drink a lot." implies "If I were in the past right now, I would be drinking a lot."
I do not agree that it does.
And the polite forms of questions are also implied conditional
"I would like to order a beer." "Could you help me?"......implies
"If you would allow me to order, I would like to order a beer."
Do you have evidence for this statement?
And "should" can even be used in the indicative mood:
"I should cook more often." (where is there any condition?)
Who has suggested there is a condition?
... it should be noted that the use of "might" [...] is really the implied hypothetical apodosis:
"I might go swimming later."......implies
"If I feel like it, or if it is possible for me, etc., I might go ..."
The implication is that there is another hurdle of choice that must be gone through to get to the simple case of "may" probability, hence a lower probability than "may"
Do you have evidence for this?