If using a record cleaning machine, can an LP be cleaned too much or too many times, i.e. causing damage to the LP? Is it naieve to think that each time an LP is cleaned on a machine, that it gets closer to being as sonically perfect as it can be, given that the LP may not have been "mint" to start with?

Assuming you're using a commercial cleaning fluid or a benign home brew, proper cleaning pads and the reccomended procedure, I doubt you're going to do much damage with any reasonable amount of cleaning. Some folks claim they use their RCM for every play. I think there is a point of diminishing returns after two or three cleanings though. I generally use a zero-stat and carbon fiber brush after and initial cleaning and will try a second shot with the RCM if surface noise persists.