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Fourth, to back up the likelihood of *médhu- and *mad being linked, we have plenty of examples of words for drink and words for being drunk having come from the same root - I've just given one example, drink/drunk, and I gave another in my earlier post, Hebrew shekar and Yiddish shiker.
As it happens, of course, English DID later borrow shekar, via Greek and French, as it appears to be the root of "cider" - oh, and "shiker", from shekar, is Yiddish for "drunk".
When my great-grandfather was eighty years old, my grandfather hated seeing him shiker.