Hmm, surprised that you found both cylinders popped your thumb up. Really expected you would find one side noticeably less than the other. Still, that popping sound you mentioned almost always means a seized piston. The only way to know for sure is to get a compression test gauge.
There are 3 separate, tightly wound coils on the stator behind the flywheel. One is dedicated to only the lighting circuit. The other two coils work together with the CDI box to produce spark. The lighting coil typically puts out 18 to 20 Volts (same with most sleds, not just Kawasakis) and the voltage regulator regulates the voltage down to 13-13.5 Volts, which is normal for a 12 Volt system. Ordinarily when you start poppin' headlight bulbs, the voltage regulator has failed and will have to be replaced. If your sled initially popped some light bulbs and then started working OK, I can't explain what happened, unless the Voltage Regulator had a poor connection, and then "healed" itself. Your earlier problem with the bulbs should have absolutely no connection with the spark, however.
Try checking compression with a gauge, double check that you have a good spark on both plugs, and we will go from there.