I suggest changing the plugs, I do mine every 5-8000 miles. If I let them go too long the bike will sputter, but typically it's when first taking off from a light and then runs fine after.
When you dismantled the carbs and pulled the jets, did you hold each jet up to a light to see if they were in fact clear? What I do is strip the insulation off of a wire and use the copper to clean out those small passages in the jets. I soak everything (except rubber parts) in carb cleaner, clean with the copper wire, then blow air through everything.
One other suggestion is to remove the caps that hide the pilot mixture screws. There's one brass cap per carb. Drill a hole and thread in a small pointed screw into the cap. Grab the screw with some pliers and simply pull the plug. Just make sure you drill only a few millimeters deep otherwise you risk hitting the screw under the cap. Those screws are turned in way too far by the manufacturer to lean the bike out for emissions control. Three turns out from fully seated is a starting point for tuning the pilot circuit. I suggest about 3.5 turns. Having these screws set properly will make for easier starts and a better running bike up to maybe 1/8 throttle. In warmer weather you won't even need the choke at all to start the bike if you have them set just right, but even just a little choke to get her started then flip it off after a minute or so is still good. Search the forum for the pilot mixture screw cap removal and adjustment. There are some threads with pictures and everything. It's really a simple task, especially if you feel comfortable with pulling and dismantling the carbs.
Finally it's necessary to sync or balance your carbs. Over time the butterflies will be out of sync from carb to carb and will need to be put back. This requires the use of a fluid filled vacuum tool and a bit more effort than the above tasks, but it's not incredibly difficult. More time consuming than anything. There are a few threads here on how to do it and also some videos on YouTube. I got my gauge for $90 from Motion Pro. It'll work on carb and F.I. bikes, 2 and 4 cylinders.
Good luck. Hope this helps. These ZZR's and older carb'd bikes can be a little finiky sometimes, but I've had my ZZR (fighter) for 7 years and 46,000 miles without any break downs or major maintenance (valve adjustments have been the only "major" maintenance). No corrective maintenance yet, just periodic stuff. Still on the stock clutch, stock fuel pump, stock fuel filter, etc. She just works.