You probably could add some U clips to the ends that are tapped. A set screw to hold it to the mirror, and then a set screw acting as leveler.
Are these plastic?
I've got some spring clips that would work like that, but thats a lot of little parts to look for in the sawdust under the horses.
It needs to be thick enough leave the jack screws in place when there not jacking and not flex when it's only supported at the corners and heavy enough to stay put when your drilling. 1/8" might just do it
The old metal Boy Scout signal mirror I carry in my tool pouch has held up for 35 years. Looks like it's about to get a big brother.