Okay, here is where I am. First, there's a lot of assumptions in this thread that don't apply to my situation. The problem is flooding/stuck float even after cleaning carb. While I will order the raptor, I'm still fairly certain that the petcock can not cause flooding if the float is doing its job.

I went out this afternoon and drained the seafoam out of the carb bowl, put the petcock on prime for a minute or so, and cranked it. After a few cranks, it fired up and ran like a charm with a little smoke and then cleared up. I suppose the stuck float will occur again, but I'm sure that has been the problem all along. Thanks for all your help.