If you get it fired up again, pull one plug wire at a time and see what happens. If nothing changes put it back and move down the line. This could rule out one cylinder problem. I think the only way it can fire at the plugs is if the distributor tells it to fire. So you can probably rule out any coil or wiring problems. It has to be firing or it wouldn't be backfiring.
Will it run long enough to get hot? If not, this would rule out carbon build up. They have to be pretty hot to fire off of that. I would think the same is true for sucking air in the exhaust from a leaking gasket.
Is it running lean? How does the exhaust smell?
Are valves in the right position at top dead center. Are they closing and opening when they are suppose to be. Exhaust should be closing just as intake starts to open with piston starting on the down stroke. Intake should just be closing or aready closed as piston starts the compression stroke. The slipped nylon ring gear on the cam could of happened. You did say you couldn't find the timing marks.
Do you know anybody with a distributor machine? You can find alot about them real quick.
If you think it could be wiring to the coil, just unhook them and run a wire from the battery to the + side of coil. ( - ) side goes to distributor. Yes, this can burn out points but not in the few minutes it going to be run.
Did you check all of the rockers and push rods to make sure one of them isn't stuck ?
Does it ever pop out of the carburator? Blow fire or fuel out?
Joe