Lozzo

First stop is check the jetting is correct. From the sound of things the main jet size seems to be about right but the needle heights may need work (the inner two jets are normally a size larger than the outer two, so don't be alarmed if you find them to be different). Also, have a look to see if it has been fitted with a Dynojet kit. ZX7Rs don't suit Dynojet kits but the Factory-Pro rejet kits do work with them. If it has been Dynojetted then you may have ovalled emulsion tubes where they exit into the venturi, and the only cure for that is to start again with a standard set of carbs and ft a Factory-Pro jet kit because their needles don't wreck the emulsion tubes like Dynojet's needles do.

Have you junked all the crankcase breather recirculation crap? That is a major cause of problems with ZX7R carburation. Google for how to do it correctly - you will need a short length of 15mm copper plumbing pipe or similar to bridge the two breathers on top of the rocker cover.

HTH