Rayjay,

What you are describing is definitely way out of the ordinary. All R* have an engineered-in shake that's almost to the point of annoying, but should remain on the side of endearing.

Yours sounds uneven and feels different every few ignition pulses. That would seem to differentiate yours from the norm. The swapping of the coils made no difference, which would suggest something mechanical rather than electrical.

What kind of gas mileage are you getting? If compression is good and it isn't electrical... think about it, it's related to carburetion and the excess fuel you're finding in the manifold.

There's no way you should be finding raw gas in the manifold.

I think the raw gas builds up, flows into the back cylinder and suppresses it, and then builds up again. If that is so, the problem would be the carb. That's my best guess.

Start with float bowl level.

However... if your gas mileage is good, my suggestion really wouldn't make sense, as your mileage should be poor if the carb is to blame.