Just a FYI for all of you:
Backfiring through the carburetor is always a timing issue. Since most if not all small engines do not have a distributor, this means it is almost always valves out of adjustment. The only other thing that can go wrong is your crank and cam shaft not being aligned correctly, and if it worked previously the chances of you knowing this happened would probably be obvious ( rod through the block ).
To be perfectly honest I am not familiar with JD small engines. But if they're a Honda knock off ( sounds like it is possible ) Valve clearances should probably be around .002/.003 intake/exhaust respectively. This of course is going by memory , and assuming the 15HP JD engine is similar to the Honda 13HP GX390. These specs are of course for gasoline/ tri-fuel models.
Anyways, just remember that on most small engines if you blow flame out the intake, the chances the valves need adjustment are nearly 100%. If it is just a pop( which is not a backfire ), it can be a few things, and the carburetor is usually where I start.
By the way, a burnt valve will most likely just cause low compression, and the engine will run either very badly under a load, or not at all period. Also I am curious about the "propane runs hotter, and needs to be retarded" comment. I definitely do not know everything, but this does not sound right. What about tri-fuel setups ? Having the valves that far out of alignment can mean a 3-5 pull start/ not running correctly/efficiently vs a 1 pull start every time, hot or cold.