Sticky Valves
The thing with valves (and trombone slides). It is best to work from the less aggressive treatments towards the more aggressive in a patterned way. That way you don't end up lapping a valve when it is the stem rubbing on the valve cap!
Toothpaste
It is often suggested that toothpaste is abrasive and would be an easy cleanup with water. Colgate Total turned up on published charts for toothpastes in the middle of the range of abrasiveness. Dabbing some on and worked the pistons back and forth for about 250 strokes each, rinsed, oiled with Hetmans # 3. It is a non-aggressive way to simulate lapping. This method probably deals mostly with tarnish.