I never wash my paterson reels aside from the wash they get with the film. The darkroom is kept dust free and I don't put the reels in photoflo either, so I might be doing things a little different.
I don't use hypo-eliminator either. I just let it wash for 30 minutes or so. That might help soak off anything that would otherwise build up on the reels.
after the film is done washing, I take it off the reel and slide it through a bath of distilled water+alcohol+drops of photoflo. Reels get set aside to dry for future use. I do this in a 5x7 tray since distilled water isn't cheap for me and I don't need a large volume for this step with a small tray.