I am believe I have reasoned out the usage of mai and mai-chai, but am seeking some confirmation.

The closest I can glean is; the single word mai is used before an action word (verb) to negate it, as in mai rue; "not know", mai bpai; "not go" or mai mee; "not have".

The meaning of mai-chai seems to be used before a noun as an adjective to state it as a negative. Like; mai-chai nak-thang-thiaao; "not (a) tourist", or mai-chai thiaao puu-ying; not (a) tourist (for) ladies.

I have also heard mee-chai, but found it is just a more formal class of mai-chai.

Any further help or clarification would be appreciated. Forgive my crude transliteration, I know with the myraid of transliteration schemes out there, there is no need for another.

Hope you can understand what I wrote.

You've already covered the most important things about the difference. ไม่ negates verbs, and ไม่ใช่ negates nouns.

However, when you want to challenge an assumption, ไม่ใช่ can be used for stative verbs (adjectives) too.

คนขับรถคนนั้น ไม่ดี = That driver is no good. Neutral statement.

คนขับรถคนนั้น ไม่ใช่ดี หรอก = (Contrary to [your/somebody else's/common] assumption) That driver isn't any good.

Note also the use of tagged หรอก in the second example, which is used when contradicting something (it can also be a softener in other types of sentences, to make a statement sound less harsh).

A very common mistake in farang pidgin Thai is to use 'mai' when negating nouns too.