First, I go ahead and use four fingers placed firmly on the film to advance it onto the reel. You're touching the non-emulsion side of the film so there's really no issues. At least, the 100+ rolls I've developed in my Jobo tanks haven't seen any issues.
At the same time, it does sound like your reels need cleaning. Soak in soap water, brush with a toothbrush, then maybe soak in bleach water over night. It also helps a lot to heat the reel with a hair dryer immediately before loading, which serves to (a) make sure there is absolutely no moisture on the reels and (b) I'm guessing it also expands the grooves just a tiny bit to allow for smoother transport of the film.
Another thing that works well is to advance the film by holding the two sides of the film, just where the reels have those two indents.