I'm happy to be shot down here, as I have almost zero knowledge of carbs on the bike, but I do know more about the ones that sit on top of a 6.6 litre V8. I figure there might be some commonality between the way they work.
I'm not sure I'll explain it very well, but here goes:
On the bigger ones that I have worked with, there are 2 ways the fuel feeds into the intake - vacuum and pumped. When the engine is running it creates a vaccum in the intake, which sucks fuel in from the carb. The more open the throttle the bigger the vacuum and the more fuel is sucked through, which in turns makes the engine run faster. When you sudddenly open the throttle there is a lag, where the amount of fuel being sucked in relates to the original position of the throttle, so you don't get a sudden burst of acceleration, but you are waiting for the vacuum to build and suck more fuel. This is where the pump action comes in, and it is linked to the throttle. When you open the throttle it squirts a bit more fuel into the intake, to cope with the lag - a bit of a boost to help things along. On the carbs I've worked on, there's a lot of tuning you can do to this pump circuit, such as speed, volume and jet sizes, which all affect the lag timing and effect of the pump.
I'm wondering it the FZS carbs have a similar function, and you're not getting the pump action. This could explain why you only see it on rapid throttle opening, but not when you open it gradually, as the lag effect will be slower/less obvious with slower throttle opening.
If it is this that's the problem, the replacement carbs may prove to solve your issue - but that doesn't mean this was the problem. The only way to know for sure would be to fix the old ones and see if it works.