It is not just the pistons that need to be cleaned, but the casings, tubing, etc. All that is difficult, so I think a good solution is to clean the pistons very frequently. They pick up "stuff" from the other areas as it washes through, and eventually it will clear up. So, no kidding, even twice in a practice session is not too often to clean/oil the pistons (or maybe twice on the 3rd and once on the other 3).
Congrats on the horn! I LOVE the bell engraving!