What's happening is that about once every 10 rounds or so I'll get a stove-pipe.
That explains alot to me. As you stated that you tried cleaning and scrubbing everything, but it still happens. It may not occur when it is clean, but after 10 or so fouling shots. The thing I would do next, is check the extractor. I think I understand what you are saying... About how many rounds have you put through it? My speculation would be the extractor is not grabbing sufficiently enough to extract the empty shell. Or, if it has anything more to do with the extractor, the return spring on the extractor may also be weak. This would cause the extractor hook to jump the shell's rim. And due to the fouling, it will only complicate the matter. But, others may have better advice than myself. I don't have any experience with that particular gun. If I were to hunt with a RF, I would stick with a bolt action all the way. But in my opinion though, there is nothing more fun than a 22 semi-auto for plinkin'. Take care, and I hope you will be rid of this problem.
Patriot