Hi my name is ***** ***** am I speaking to ?
Answer to your question is yes, there is accelerator pump that is controlled by a diaphragm, not sure if these carbs have been gone through lately, but given the age of this unit I suspect that the diaphragm has likely failed.
Also if the bike has been sitting the passage ways could likely be clogged for the fuel becoming unstable, so you could actually have something of that nature going on also.
Changing out the handlebars shouldn't have anything thing to do with a runnibility issue, the choke on these carburetors are not cable operated choke so you can rule that out,if anything I might contribute it to being completely coincidental.
I would start with pulling the carbs and then professionally have then gone through, also you might peer into the fuel tank and inspect for any internal rust on the walls of the tank, these tank are just metal and not coated, and over a period of time they can rust and then that finds it ways into the carburetors.
Let me know of this helps, or you have any further questions.