something aint right .. although i'm very familiar with my carb and could probably assemble it in the dark, first thing i'd be inclined to do is take the thing apart and reassemble it again..
the bike runs alright at higher speeds and that says two things.. ignition and compression are ok. The only reasonable thing left is carburetion.
Did you use any gasket compounds on the carb itself when you reassembled the carb? Did you do anything at all out of the ordinary or are any carb gaskets or parts altered in any way?
btw, when exactly did this problem appear?