Decided to try again with the mirrors.

This time I cut them to size first, and then used actual paint stripper to remove the back coating.  The results were fantastic.

First cut them to size and sand the edges with silicon carbide sandpaper.

Then wash them in soap and water.

Then give them a generous coat of paint stripper in a clean environment (unlike mine).

I got lucky.  I realized as I was wiping them down after stripping that the little flakes of glass I had created from cutting/sanding the edges could easily ruin the silver.

It took two coats of paint stripper, and a gentle wipe with some paper towel after each, over the course of 30 minutes.

The stripper left a residue on the silver which was easily removed with some alcohol.

The reveal:

Holding them up to a bright light, I did a whole lot better this time.  No scratches/holes in the silver from me rubbing too hard like last time.

Now to install them in the arm.