grammaticality - Why Is "You did well." Even Grammatically Correct (American English)?

The reason is less one of grammar and more one of the various different meanings of the verb "to do". Although we think of "do" as being a catch-all, usable-in-all-situations type of word, in fact it isn't: each meaning of the word is very precise and requires its own particular grammatical structure to be acceptable to an English speaker.

So when you say you did well, or poorly, or splendidly, you are effectively saying you "acted" or "performed" well (or poorly, etc.). In my Shorter OED this is meaning II.1 ("To put forth action; to act") or II.2 ("To perform deeds; to work"). A slightly different meaning of "you did well" is to have fared well, but still the general notion is the same.
However, just because the word is understood to have this meaning doesn't mean it is synonymous with the definition: you may have acted properly but you wouldn't say "you did properly".

The question of grammar returns as a secondary consideration because this version of "to do" is clearly intransitive.

"You did good" is a quite different meaning, and equally clearly transitive. "To do" in this sense means "to bring into existence" or "to accomplish". And although we are far more tolerant of generalised usage of the verb in this sense, we still insist on differentiating "do" and "make" in numerous cases: you did 50 mph but you made record time, you did the dishes but you made dinner, you did wonders but (if you were a powerful ruler many centuries ago) you made wonders.

Finally, looking at different dictionary definitions of "do" gives further proof of the highly specialised usage of each sense of the word over time. My 1933 edition of the Shorter OED groups all of the above transitives in definition I. This includes doing a speed ("do a mile a minute") or doing a good deed. The online definition linked to above, however, splits many of these uses into quite different categories.

So although some might claim that "you did well" is a special case, it would rather seem that most of our current uses of the verb "to do" are special cases in themselves. Grammar tells us how to do "do" well, style guides tell us not to do "do" too often, and changing speech shows us how we cannot (literally) do "do" to die, we can (figuratively) do "do" to death.