Jeff, No, I'm not sure if the float is the issue, I just know that a bad or mis-adjusted float can cause carburetors to act strangely and that float replacement is often overlooked. I didn't know a float could be a problem until someone told me. If it is the black plastic type, I would replace it just because. If it is a copper or hollow one, I would test it in gasoline to see that it wasn't leaking. And whatever kind it is, I would make sure that it was adjusted to manufacturer's specifications. If your rebuild kit doesn't have instructions, there are manuals available in the Manuals section off the main forum page. Adjusting or replacing the float is something you can do without removing the carburetor from the engine.
However, I can't help feeling that your problem could be mechanical. If an intake or exhaust valve is sticking, I'm wondering if that isn't the cause of your problem. Or perhaps one of the head gaskets is leaking.
Have you pulled both spark plugs and compared them? If one of them "reads" significantly different from the other, that would indicate a mechanical problem in one cylinder, not a system-wide fuel problem.
Another way to verify the condition of the motor is to check the compression of the cylinders. They should be within 10 lbs of each other. You might want to check them cold, and then check them again when they're hot.
What's driving me nuts is that I remember having to choke my machine to get it to run at one time, but I can't remember what the problem turned out to be. For that engine, I remember that I didn't have my float adjusted right for a long time, and I remember having a problem with sticking valves, but I can't remember at what point I had to run with the choke on.
I would still start with the float. I could always tell when the valves stuck because the motor turned over faster but would never start until the engine had cooled down for at least 30 minutes. Oh, I remember how frustrating it was.
Anyway, good luck. I don't feel that I've been much help to you.
Again, please post your serial number on the main page and someone will help you identify the year your machine was made and help you more than I can.