I would start by adjusting the valves, and then checking compression. If you have a burned the intake or carbon deposit build-up on the intake valve or seat it will backfire. Also change sparkplugs as deposits on a plug can lead to popping through the intake on a hot engine.
These engines also get carbon deposits on the cylinder head and on top of the piston if they are not worked hard enough over a long period of time, or used in a lot of short rides. If backfiring occurs after the unit is fully warm and run for a bit, then it may need disassembly and decarboning. I see this situation on units used for hunting where they are just putted around at slow speeds and never worked hard enough when they were new to fully seat the rings.
A failing diaphragm on the air cut valve on the carb (the small air valve on the side of the body) can also fail and cause backfiring. This is usually the cause if the valves are properly adjusted and compression is good.
A leaking air line can be the cause of backfiring. Not probable unless someone went after the positive crank ventilation system and removed or rerouted lines without being very careful.
Cold engine backfiring can be from a worn or misadjusted fuel primer (choke).
I would rule out slide wear being your problem. Worn slides lead to power losses, very poor fuel mileage and lousy performance, but seldom to popping out an intake. If the diaphragm on the slide is leaking from a crack or loose that can be a cause of firing back through the carb, but will generally occur when you "honk" on the throttle under load and have it pop a short time until the slide equalizes. Running with one doing that over time will burn an exhaust valve and cause low power and compression.
Because of the need to run through a very prescriptive process of elimination, these newer big twins really need the repair manual handy as you do your adjustments and process of elimination.
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