I’d have to see some concrete sentences, but I think your rules are right.
There are some quantifiers, such as “the majority of”, “a minority of”, “a number of”, “a lot of”, etc., that are transparent for the purpose of singular/plural verb forms, so you have to use the verb form that corresponds to the noun that comes after “of”.
I just want to make it clear:
“A lot of” can be followed by a non-count noun, but surely “the majority of”, “a minority of” and “a number of” can’t do the same, right?
And when we say “The minority of …”, we do refer to a number greater than one, don’t we?