Found this on Z Power site:
The GPZ was fitted with a set of four Keihan CVK34mm carbs, which were normally excellent in operation, but it was noticed that sometimes there could be a slight hesitation at low engine speeds, a bit like the lag that we used to get on the injection models. Kawasaki decided to modify the needle jet holder allowing more fuel to pass through it. The new part number for this holder was 13091-1347.
This went some way to eliminate the problem but some owners were still complaining of flat spots at around 3,000 rpm and erratic tick over. Inspection of the carb diaphragms verified that they could twist in the carb bodies so Kawasaki modified them and fitted them under warranty to all affected bikes. All new bikes after frame number 015192 had these modified parts fitted at the factory. If you need to check to see if yours was done, there was a blob of white paint on the left side of no.1 carburettor.
Sounds just like my bike.My carbs are off maybe an 86/87 model. Have to look here.

2 X ZRX1200R 4 X ER6N, GT550, 1988 ZX-10, 4 X GPZ250R, 4 X GPZ900R and GPZ750R

Yeah I like Kawasakis.