sounds like messed up idle jets to me.
the idle jet fueling system is tiny and it is placed downstream from the throttle plates (closer to the engine), to allow it to take advantage of every bit of vacuum that the engine can generate at the relatively low RPMs you get while cranking (which, of course, is going to be much higher when the throttle plates are closed). opening the throttle plates just dumps all the vacuum away.
the idle jets are very small items, located toward the engine side of the carbs. a couple of months ago I disassembled a set of Bandit 400 carbs (BST32s) and when I took out the idle jets they were very crusty looking, and not just the needles but the tiny little emulsion tubes that go with them and the springs and the tiny rubber o-rings too. and this was on a bike that would always start pretty well, but that's what you get on a 22 year old bike.
I know that nobody really wants to open up this can-o-worms but on a 22 year old bike a careful cleaning of this little fuel circuit could help. although, once you have the carbs off the bike you might as well go through them completely, right?
I'm more familiar with Keihin carbs. Mikunis seem to be a better product overall, for performance, but they have more intricate plumbing than the Keihins. I guess that there's probably nothing better than a perfectly clean, well tuned set of Mikunis and nothing worse than a gummed-up, neglected set.