I had the same issues on 500 I bought this fall. Thought that the carbs were dirty, old gas, old plugs. step 1, I cleaned carbs put new plugs and good gas. Still backfired on the PTO side. If I disconnected the TPS sensor on the carbs the backfiring would stop, Check carb sync and tps both ok. I moved carbs from onr sled to another ( 3 500's in the garage ) problem remained with the sled, then I tried a wire harness and the problem seem to go away, I ordered a new harness and install. The problem came back. After playing with this sled for a complete day I found that when the engine temps ran 150 degrees the backfire was very slight but would be bad at startup and until 150 degrees. The problem was crankshaft indexing and a bent rod on pto side.
My suggestion would be to check the carbs first and then the crankshaft indexing, if I would have done this in this order it would have saved me a lot of time