Double side tape on the dry side is a great idea. Wish I had thought about it with mine. I understand the worry about taking paint off if you move it.
I used acrylic sheets on the dry side and cut out circles the size of the dry side. I mounted that acrylic up against the glass so it supports the dry side so it can’t slide down.
Not sure if that would help your issue with the magnets not holding well enough. It would take some pressure off. You could even strap across the back of the dry side so it can’t fall out.
The only issue then is securing the acrylic in place.....and you’re back to the double side tape issue.
Or get creative securing the acrylic. It’s a more complicated solution.
I like the double side tape option. Simple. Smart.