Just wanted to post an update on that topic.
I found myself a set of CV32 keihin carbs, stock for both the KZ400H and the KZ400 B, which I installed on my KZ (the airbox is the 400H one, as I have a KZ400 B engine in a KZ440 frame - the KZ400H airbox is the same as the KZ440).
The bike now runs great !
I just had a slight blip off idle, with the engine stuttering when I started opening the throttle but after adjusting the float level, it is now perfect through all ranges.
Another problem I encountered that could be of help to others is that when I first installed the new carbs on the engine, it acted as if there was an air leak. When setting the idle, I couldn't bring the idle back down, even by closing completely the idle screw. Turns out one of the butterfly was bent and letting fuel in even with throttle and idle screw closed. So if you encounter that problem and can't find an air leak, could be this !