If it's the stock Mikuni flat slide, I think it's a 38mm, and with the lever up, it's on. Man I wish I could post pics. I have that carb on my bench right now. If it's that carb, take it off, put it on the bench, leave it there and go get a big keihin PWK and a 180 main jet and about a 62 slow jet. Set the needle at the middle position and then tune from there as needed. Check the Salvage yards, craigslist, old motocross guys have them laying around. They are much easier to tune IMO than the flat slide Miks.
The excessive backfiring sounds like a plug that's way too hot, or timing is off. Buy a flywheel puller. They are like $15. Make sure the flywheel didn't spin out of time. Then make sure the timing marks are lined up with the center of the screw holes where the stator mounts.