RE: BME-44 backfiring
I had the same thing happen with a new 3.2 Brison. Ran for a minute or two then staring doing what your is. Terry at CH strongly suggested that the carb was the likely cuplrit. I still haven't installed the new carb that Brison sent me yet, so I can't give you anymore than you already know. I suspect the same as you though, that the advance isn't working.
If you find the problem before I do, would you mind sending a PM to me, or posting the cause here?