The pops in the muffler suggest that the exhaust valve is leaking, or the spark plug is faulty, or either the valve timing or ignition timing is wrong. Coupled with the fact that it is slowly improving, and it had apparently been unused for quite a while before you got it, my first bet would be leaking valves. This is usually due either to them not seating properly, or (perhaps more likely) sticking in the guide just before they close. It is a problem that needs to be fixed.
Also, with regard to your issues with the coil-to-flywheel gap, I suspect you were following a red herring. Refer to this Briggs FAQ:
http://www.briggsandstratton.com/us/en/support/faqs/ignition-system-theory-and-testingIn particular, consider this part of the answer:
"An armature air gap that is too wide will prevent spark. Not true. Well, sort of not true. Briggs & Stratton air gaps cannot be made too wide to prevent spark providing the coil is healthy and the engine is spun over fast enough. A wide air gap, say .030" will ever so slightly retard the ignition timing as the magnetic field takes longer to build within the coil windings."
