The main jet only affects midrange and up, the pilot circuit and jet affects the off idle up to midrange.
My opinion would be to find out what stock setting were for everything. jet sizes, air screw position, needle clip position, disassembly it, and blow out every oriface in the whole carb, then set everything to stock. The float level should usually be level with the carb body when you hold it upside down.
Make sure your air filter is clean and oiled, and that the exhaust isn't restricted with carbon (Does it have a spark arrestor that could be clogged?). Make sure your choke is seating correctly and that the plunger is stil lin good shape with rubber in the bottom to seal against the choke opening.
If you messed with timing, also set that to stock as well. That can cause bogging/backfiring. Check for good consistent bright blue spark.
If it still doesn't run right...
You might have a failing coil or stator. Not sure if these can cause intermittent issues or of they just fail and you're done. You might want to a search on symptoms of bad stator, but I remember hearing about backfiring and bogging etc. It could also be engine related, leaky seals etc, but usually that makes things run lean and more snappy than normal...
Hopefully I didn't just run you around in a circle. Just some things to check out. Usually, when I pull things apart, clean everything and reassemble to stock settings, it works, even if I didn't really find a noticable problem during the process.
Good luck.