Let's just say I ruined some trim.
Oh well, the trim I have isn't the best anyways.
Don't try this at home, kids....
I was able to carefully take a small drill bit and drill down at the angle the glass allowed to anchor some of the clips,
but that put the original clips too low really so the trim sits too low there.
This didn't work in the corners, especially the lower corners though, as you might expect.
The corners, where the vertical and horizontal trim meet and overlap, are currently held in place by a couple tiny stainless
screws.
Yeah, I know. Yuck.