Also, you need VOM meter attached to measure for short on wire loosened from coil, and start wiggling things to find what remove the short like resistance of ZERO ohms.
Chase down the wire to find where center conductor touches ground and kills spark. You have problem in hand. Some sort of grounding device/switch or wire bare some place for OFF. Sometimes putting it back together and "all is well"!
Where are you measuring exhaust temp? Normally measured near cylinder. Normal would be small hole about 3" from cylinder with thermalcouple probe about near 1200°F. But if on outside tubing little less. Heads less than 400° F (200 maybe idle). What adjustments on carburetor, maybe only 1 idle...
Cracked/broken cylinder ring. But need good check on intake to that cylinder.
Backfire and popping sounds like lean running. You might run engine with some choke and see what happens. Bad cyl temp increase while good cyl decreases?
Also check head temps both cylinders after warmed up...
Check valve clearance adjustment, especially if overhead valves. All of these type loose adjustment and severely disables the compression release on startup. Normal valve clearance is small and subjective to wear. Briggs and Kohler
Check the valve lift. Should be around 3
They should be removed and a proper size reamer used on valve guides. Guides build up deposits so diameter shrinks and valves then sieze. Even 7 thousanths is slightly high. Flat heads have larger clearance than the newer overhead types.
About twice too much clearance. 3 to 4 thousanths more normal for these overhead valve engines. Valve adj controls the compression release. So valves open slightly before piston at TDC (max compression). Valves to loose (big gap) they release to much of compression so cylinder will not fire. And...