Here is what I found, and it appears to be working just fine. Just experimented with 1 door, and has been about 17 hours.

It's called Peel & Stick Caulk Strip for tub & wall. This particular brand is Homax, and I found it at Lowes. It's 7/8" wide, but only 1/2 of the strip had adhesive backing, which was perfect when I cut the other 1/2 off with a razor. The strip is about the thickness of a piece of notebook paper, and after trimming off the unsticky side, width was perfect for the 1/2" chrome molding.

Making do with what you got, is definition of Hot Rodding, IMO.
I will let you know if it fails.
Thanks everyone, for chiming in and offering suggestions.

Jack