“cheese” is (often) uncountable, and with uncountable nouns there’s no problem in “different kinds of cheese/money/cancer/information.”
I don’t have a problem, though, with, e.g., “There are many different kinds of bicycle.”
Is the explanation here that in such cases (i.e., a normally countable noun being used in the singular after “many kinds of”) the noun is being used uncountably, i.e., as a mass or generic term? I feel that might be it.
Personally, I have no problem, in principle, with “many different kinds of method.” I'm not sure I would say it's always interchangeable with " ... methods," though.
(b) (OP) would be wrong, unless preceded by an article, probably indefinite. But then “method” would have to be singular.