I don't have any experience with the Chuck Harris mirror. I had an excellent mirror of this type that I got in 1980 or so; the mirror was a lucite disc with a groove machined into the edge, and the end of the wire was bent into a circle just a little smaller than that, so the wire held the lucite mirror snugly and firmly (until it didn't; the mirror fell out a few years ago. Cheap **** didn't even last 40 years! If I were making myself a new mirror, I'd try to replicate that one.
I don't bother making them for myself, though. These are better than what I could make:
https://www.ebay.com/itm/33404809845...UAAOSwOvJe2fB9
They don't last for ever. I got three of them a while ago, and am still on my second one.