Well, I just replaced the entire fuel system. I verified the Gas tank is clean inside, that it is flowing fuel out fine. I replaced the lines all the way to the carb. New Fuel Pump, and new fuel filter. It is still doing the same thing. I went ahead and threw the in-line spark tester. The left side spark is constant, even when the power cuts out briefly. The right side is not as constant, and when the power cuts out, the in-line spark goes away briefly, then cuts in again and the motor comes back up.
I did not tear into the carb today, but I am not sure that is an issue here. I will probably attempt to get at the solenoid and do a carb clean tomorrow. I have a multi-meter, is there a way to check that the ignition coil is actually bad? I'd rather test it first then spend 50$ on a guess/misdiagnosed part.
EDIT - For some reason the comments after my last post did not refresh until I just posted this. Didn't mean for it to sound like I was ignoring anyone, I appreciate all the advice and help so far