Thanks for all the tips. This proved to be a chicken & egg problem. The trim would come out a lot easier without the glass in there, and the glass would come out a lot easier without the trim in place. I finally managed to work the trim free of the gasket toward the bottom; the brown piece is a cabinet leveling shim which helped to pry it free. With the trim about 2/3 free, there was enough stretch in the gasket to get the glass out. The remaining trim then separates easily from the gasket.
What I didn't expect was that the trim is a one piece weldment. It looks like four separate pieces from the outside, but it's not.
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