I think the best solution is a mirror cell that the mirror can't fall out of, regardless of orientation. That way you're covered when the cleaning lady points the tube toward the living room floor while you're at work.
I remember a conversation with Ed Beck about 30 years ago. He hated getting mirrors to refigure (and send off to coaters) that had silicone adhesive on them. He said the coater hated cleaning them before putting them in the vacuum chamber, because sometimes it wasn't obvious there was any, when there was.
I just don't have the patience to wait for it to cure. So, what have I used?
On my 10" mirror, I used double stick foam tape - the stuff from 3m that's used for affixing weatherstripping on the side of a car. BUT, the cell also supports the sides of the mirror as well as the back, and the foam tape is also around the sides of the mirror, so getting the mirror to come out would involve shearing the foam tape. I haven't had any problems with it in the 8 or so years it's been like that.
I chose the stuff because, when I stupidly broke the windshield on my VW Eurovan about 10 years ago (by putting 12' 2x10s on the dash and closing the back door...), I had to have the windshield replaced. The guy had to take the air dam off the front of the van (looks like this one: https://uploads.tapa...e5892034112.jpg). But he just stuck it back with the old adhesive, and it started to come off. So I bought some of the 3m tape, cleaned the mating surfaces with acetone, and stuck the air dam back on the van. It hasn't shown any signs of separating in 10 years and about 100K miles of driving. I like to drive 75mph on the interstates, and it's often over 100 degrees f out. And I've had some serious headwinds from time to time over the years. So there's some serious force against it for sustained periods of time.
Still, I'd never rely on it solely to hold a mirror in place. Clips might be annoying, but not when they're needed and do their job.
If you're going to use tape on plywood, polyurethane the plywood first.