I have the same exact bike, same kind of problems. Mine has new replacement carb last spring (2020) runs fine idles good, run thru the gears. But after a few miles and it gets hot it turns to crap. It will stall if you don't keep giving it fuel and kind of loses it's HP, doesn't seem to run right and you have to park it. I think it's the choke thing. The replacement didn't fit exactly and I couldn't get the choke cable to sit right.
The Big problem is you can't get at the carburetor with out dismantling the airbox. Not even to make idle adjustments. And even then it's extremely hard to access.
Time for a new one after 21 years.
Any suggestions for a new quad?