OK, well we need to figure out where to start. If you are not 100% sure there is a engine issue, get a clean pan, and drain the oil, inspect the oil just to rule that out, if you have a clean pan then you can dump it back in the engine, no sense in wasting good oil.
Second, you'll need to ride the bike, I have a timing light that I have used in the past, where I have hooked it up and drove the bike with the timing light on, then when the engine start to act up you can actually observe the light and watch for any inconsistencies, that would indicate you have a spark issue ?
This is likely a California model as your location, so if its running the charcoal canister then you might have an issue on the vent line ? This model also has a pet-cock but also utilizes a vacuum control for shutting fuel flow off to the carb, I have seen those in the past act up and limit fuel flow.
Lastly if you have a second key, put it in the fuel cap, when riding and the unit start to act up then pop the cap, if its a venting problem then likely the bike will pick up and go, I have seen that the reeds in the fuel cap get stuck from unstable fuel and that don't open, you could have something going on in the cap.
I'm giving you something's to try so I can start my thought process as to what direction, as I right now we haven't ruled anything out.
So you might have to try this tomorrow and then get back to me, I'm in South OC