I wonder why you guys think so complicated, the main problem lies in the drummer, hat bashers will never get a good sound.
The second problem is the hi hat, bigger hats sound less loud than smaller hats. My favorite hi hat is a 15" zildjian, if it's too loud put a number of coins in the bell of the lower hat, that'll make it softer sounding. (this is a Steve Albini trick)
The third problem is the snare mic, the SM57 is a decent mic but it has a nasty off axis response, so the hat bleed will sound bad, really bad. A Beyerdynamic M201 is much more rejective and has a nice off axis response, this mic can solve your problems.
Don't even think of recording the hat separately, this is how you'll kill the groove.
Forget about gates and expanders, it'll make your snare sound bad, sometimes they will work on toms.
The best advice I can give you: get a Beyer M201.