Without a factory service manual in front of me, I'm just throwing this as an idea to a possible cause? or it could be some other related safety switch inline the ignition circuit harness.
Just curious if the your quad was equipped with some form of (ETC) Electronic Throttle Control switch, like a Polaris product would be equipped with. Or some form of 1? used by Suzuki. In the advent the throttle cable breaks or becomes stuck or out of adjustment the ETC kicks in, Grounding the CDI BOX out. I had this problem before on my 01 trailboss because the cable needed adjusted. normally it should of just killed the engine going from idle into "mid range" throttle. but the switch contacted ground intermittedly (causing backfiring) when it should of just killed the CDI box all together at mid range throttle if adjusted correctly.
Knowing you already checked the , 1) In & Ex Valve clearances, 2)Spark Plug resistor cap (Rx Value), 3) Spark plug, even though new? got some out the box that were bad. Flywheel Key half sheared due to the back firing, Flywheel Magnets (magnetic poles become unstable to be not useable). Even if a ignition coil tested good, seen them also cut-out when accelerated due to a internal crack inside the field windings which you can or cannot see. The Stator plate and alternator windings for shorts? After the wiring harness being cooked, your lucky to have spark, depending how good of condition the CDI box and pick-up coil in the stator are? after the fire. Finding were the previous owner left off?, is real treat or sometimes a real headache.