ok I might be totally off topic but what is the reasoning in an over the top RL, I might be wrong but having it under lets you hang stuff to dry and helps support the tarp (I think) so why use an over the top

back to the main topic:
I've used both full RL and only the ends and I like them both
as far as not damaging the trees, why not get the tube straps ( I don't know the real name, sorry ) and insert your Rl rope in it, you can then adjust the RL without hurting the trees, not that much as far as weight penalty, even less than opting for tree huggers, doesn't even have to be really long, a couple of feet on each side will do the trick! and it will even protect your line if the tree has coarse bark