Well, I tried the tape thing on the inside of the pump handle, and it didn't quite work out. It was slick for sure, but I think the tape I was using was a bit too thick. Even with only two strips inside the handle it was too tight of a fit, causing the pump action to get sort of hung up with a lot of resistance.
I think I'd be willing to try it again, but I need to get thinner tape, probably 5 mil. Until then I'm just gonna apply a light coat of pb oil to the outside of the barrel and try my best to keep it clean. I'll post an update if I find some tape that works.