You're welcome! First thing to mention is that the timing chain is the least likely cause of your issue... even then only as a contributor, not the cause.
I am assuming that the two carbs you have had on the motor are both OEM. Let us know if that isn't fact?
First things to suspect would be a failing or mis-gapped (very tight gap) spark plug (new Champion plugs are the worse offenders, buy NGK to fix), sucking air through a cracked or warped intake manifold, spark plug cable deteriorating or pulling apart from the boot, etc. It can even be a bad CDI but don't jump to any conclusions with that... odds of a bad CDI are a long shot bet, and may waste your money chasing that ghost.
It can be a combination of things adding up to cause the problem too. First thing to do is make sure the intake is not leaking between the carb and the head. If there are any issues in the motor (bad or worn out valves for instance) those oddball issues can be contributors to other problems and make diagnosis a bit more difficult.
What year is your 300? Is it all stock? Any non-OEM replacement parts on it?
EDIT:
Check all your wiring harness connections too. They must be clean and tight, no moisture in them. Check the ignition switch and kill switch too, if the spark plug and intake are proven good.