Is this not a very expensive way to solve a problem that could be addressed much more simply by just using a large flat mirror to capture the view that we want the telescope to look at?
We do know how to make very reflective large flat surfaces as well as how to point them accurately. The mirror can stay flat on the ground, only the flat reflector moves.
Seen that all the objects are at infinity, any distortions introduced by the reflection should be easy to eliminate.

If the tree rings "diverge unexpectedly from the actual temperatures" recently, how can there be any confidence that they did not do as much in the past? Consistency is lost here.