Tanker,
What I do for my Uberti Remingtons is to keep a small plastic squeeze bottle in my shooting box and between stages, after charging & greasing all loaded chambers I put a single drop of oil (I use olive but others like Ballistol) right at the juncture of the cylinder front and the frame. I then jiggle or twirl the cylinder a few times (holding the barrel up) to work it onto the cylinder pin. This 10 second procedure gets me through another stage or two without beginning to bind. If I'm shooting full loads (30grs powder) I do it each stage if shooting light loads (20grs) it's done every 2-3 stages. No need to pull the cylinder and get all messy. Save that til the final after match cleaning.