Auch zweimal Plural, würde ich sagen: two different kinds of methods

Bist du da sicher?

Wenn ich "types of cheese" sage, meine ich ja auch mehrere Käsesorten und nicht nur eine, und trotzdem steht der Käse im Singular.

“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.

I don't have a problem with "different kinds of chair," either---and my feeling is, as I say, that "chair" here is functioning, or being made to function, as a generic (hence grammatically uncountable) and not as a countable term. What I'm less clear about is when I would use which. "There were all sorts of different kinds of chairs spread around the room" sounds right to me. "Different types of chair are suited to different human activities, e.g., working, reading, snoozing, etc." seems right to me too. And I feel I'd likely select those forms in those two sentences. I wouldn't want to say that using the other form in one of the sentences would be wrong.

Oh, right. It didn't occur to me to see chairs as an abstract idea. I was thinking of real chairs in real rooms. Your second example doesn't sound weird to me either.

But "all manner of things". I think "all kind of" is probably OK too.