After reading the thread on back up knots I got an idea. IN the thread someone suggested clipping a biner through the slip-knot making it into a marlinspike hitch. That's a good idea.

Here's the next step, thrown out for your speculation.

Around the _base_ of the tree there would be a rope that has a lot of loops tied in it. Think of a daisy chain long enough to go around the tree.

As the climber moves up a loop knot is tied in the tail of their rope. Butterfly knot would be good or even an overhand on a bight. Then, the biner is clipped to one of the eyes on the anchor rope.

One limitation is that the climber wouldn't have any extra line below their hitch to tie off any other safety knots though. It would be a sure way to keep ground-falls from happening though.

Tom, here is the system we use. We have a piece of webbing tied to the trunk of the tree (at least 3 wraps around), tied with a water knot. Then as the climbers go up, we periodically put a safety loop in their downrope and clip that loop to the tree with a non-locking biner.
NOTE: When we do programs, the climbers are climbing on a DdRT system using a Blake's hitch.
Clipping to the tree makes it much safer for the climbers because they can't come down all the way to the ground; their downrope is clipped to the tree.
Patrick

You can see a couple of ropes clipped to the tree in this picture.