my guess is a float level issue.
depending on how in a rush you are to fix this, you can try the easiest method first, which (and i hate to admit this) would be running through the carb with some cleaner like seafoam.
i had a similar issue with one of my other bikes that resulted in my girlfriend's leg being doused in gasoline at 50mph (and she hasn't been back on since
) and it turned out the floats had sprung a leak.
carb kits... i'm not sure where to pick them up or what comes in them. gaskets maybe? maybe a float valve? anywho, if you can spare the time, i wouldn't buy one until you know you need one (e.g. you've discovered beyond a reasonable doubt the source of your problem).
if you have more time, you could rig up a float level checker (clear plastic tubing tied up to the bowl drain) and see what levels are while the bike is running (hint: they shouldn't be higher than the bowl is itself).
i've never heard of a choke lever causing gas to run backwards, but who knows, i'm not the most experienced one here. all i can say is that the choke has never been suspect on these forums before. petcock, floats, and clogged carb orifices have been.
shoot us some pictures and maybe we can help out a bit more.