A couple of rap rings tied into that rig would help with the friction problem. They are pretty cheap, and would make for a reuseable setup. One could use some small perlon to hold the system around the tree, small enough that the tree would easily break it with growth. 
  
Which makes me wonder: wouldn't the rope pull the rope-loop pictured down after one rappel, making it litter? What if everyone did this every time tey rappelled off a tree? It would make for a lot of scattered rope/webbing, it seems.  
  
I have seen rappel systems that are retrievable. I can't think of the set-up right now, but I am sure one of you has the knowledge/link. Anyone?