isn't "Nobody knows me as well as you" a bit strange? Sounds like: Nobody knows me, including you.
Notice that "DO" at the end of the sentence.
Similarly the Czech sentence can sound "Nikdo mě nezná tak dobře jako MĚ ZNÁŠ ty". "Mě znáš" is just often unspoken.
Wouldn't "nobody knows me as good as you do" be also correct? Although I know 'well' sounds better.
Your suggestion is definitely incorrect. English requires the adverb "well" here, not the adjective "good"'.