I say your timing is out if you only getting back fire, the pick up can slip on the tapper if its not sitting right in on the tapper be the first place I look and reset the timing you won't know if its slipped till you take it off the end of the cam, when I installed my Joe Hunt the tapper kept slipping and putting my timing out after it had fired up and running then slip and get the backfire and no go, the cause of the tapper slipping was it wasn't sitting fully home no matter how tight I do the bolt up, after putting bearing blue on the tapper I found out where it was sitting and was only on the edge, how did I fix it???
I threw the tapper shaft for the JH in the freezer for a day or so and when I reinstalled it I had all my timing mark set, put the tapper shaft where it was set for timing while it was frozen and gave it a good whack and then tighten up the bolt, hasn't moved since and if I need to work on the JH I can remover it without touching the tapper drive shaft, that was over 14 years ago and I can still remover the timing cover with the shaft still installed, but the tapper shaft is the same tapper on the pick up stator of your EI.
If your plug is sooted up badly then that tells you what cylinder is giving you troubles and can also be sign your pilot jet is blocked on that side carb, but it should fire up on one cylinder as mine does with the JH maggie when my pilot jet was blocked, took me 2x pulling that blocked carb off and poking the wire in the pilot jet gully before it shot out after hitting it with the compressed air, it shot out with force and was like someone stabbing my finger with a sharp needle where I was covering the hole.
So I be looking at both these areas, carb and tapper on the pick up, the sooty plug getting fuel the clean plug is not getting fuel or something like that.
Just because you own British bikes before it seems you have never had this problem before, take each step at a time trouble shooting can only be a few things, timing, fuel, bad battery, wiring, a bad battery will cause back firing under load, even near new batteries can fail why most battery suppliers only give 6 months to 12 months warranty if you are lucky.
Ashley