I was able to fix the rotted foam behind my center vents without removing the dash. The louvers and their immediate surround will come out from the front.
Spent some time with small tools, brushes, Q-Tips, and solvent, cleaning the remaining gunk off the sheet metal flap.
Once the flap was free of gunk (but not cosmetically attractive), I brushed on some flat black Rust-Oleum paint through the opening.
I then applied some peel & stick black dense foam tape around the perimeter where the sealing actually happens, leaving the rest of the flap with just the new flat black paint. The tape is not at all like the original foam. I got it from a large auto/truck AC specialty shop. Though they told me it is not sold seperately, it comes as part of the installation material with various AC components. It's actually considered an insulating wrap. They told me most shops keep leftover pieces around and I was given my piece free. It cut easily with ordinary scissors and they told me it would not rot like foam.
If I hadn't gotten the material from the AC shop, I was going to look at peel & stick insulation strips for home doors and windows.