Do you have any *old* Paterson reels, or can you borrow one from someone? If an old one does not have the problem *in your darkroom, with your water and chemicals", the problem is (obviously) with the new reels.
I have an unused Paterson reel as well as several older, well-used ones. The "new" one (I have no idea when I bought it) is slightly different: It is, of course, not yellowed with use. The little ball-bearing is held in place differently (merely snaps into place in the new version). The radial ribs is narrower, and one says "Paterson" on it. The old ribs have shallow V-shaped channels or grooves on the outside, one per rib. (I have no idea what they are/were for.) Visually and by touch the material and general finish seem to be the same. It does not seem to have any manufacturing residue, but if I thought it did I would wash it as you did, and then wash it again with some other mild chemicals: rubbing alcohol, TSP (tri-sodium-phosphate), acetic acid (vinegar). . . After all of that, if you still have those sticky bubbles with plain water you might try a wetting agent, just to see what happens.
Back in the late 1970's photographers were often advised *not* to use PhotoFlow in film development tanks or with reels because it was difficult to completely rinse off and could affect sensitive developers the next time you used the equipment. That may have been an urban myth, though. Edwal produced LFN for the express purpose of reducing any possible interaction with developers, hence the initials: L(ow) F(oam) N(on-ionic) wetting agent. Whether it works as intended was disputed 40 years ago, and a check of web discussions shows that people still disagree. It might be worth a try, though. I would first try it in the pre-soak step, 1 or 2 drops per litre.
Kodak's HC110 developer could be awfully foamy, but I could avoid problems by always presoaking the film (1-2 minutes), pouring solutions in carefully (think of pouring beer), rapping the tank at an angle, and spinning the reels back and forth a couple times (if I hadn't misplaced the Paterson spin-thingy!). It also helped to have an enough solution to leave only a small air space for agitation (not too much, not too little).
Good luck!
BTW, do you get bubbles with all of your processing chemicals? That is, are bubbles a problem every time you pour in a new solution?