Any ideas how to buff out the scratches?
gas...
This is a long shot, so test it first on something else....
Go to a craft shop and buy some liquid catalyzed epoxy. I have used this quite a bit in my woodshop.
Mix it up, put it on, and immediately wipe over it with a squeegee to get the effect you want. There are some potential issues...such as...
Can't use a towel/rag with loose fibers...the fibers will be "in the mix"
It tends to bubble as it dries if you put it on thick...but yours should be thin
It's messy...cover anything you don't want it on
Only mix tiny amounts for your application...but measure it...the mix is critical
See my wood details thread for some discussion of where I've used it.
Another option if the scratches are very light might be those "sticks" sold on TV to fill scratches in glass...dunno.
Good luck.
Dave