I started cleaning a small area using a paste made with Bon Ami
and water. Using a sponge and rubbing horizontally. Messy job.It cleaned 95% of the stuff off of the grid in that area. Looks pretty good. Not good as new. But acceptable.
I didn't think to try ammonia. I'll pick some up to check it out.

I pulled the rear shelf out to give me better access to the entire glass.
Going to see someone tomorrow about a dye job on the shelf and the fabric trim around the doors. Palomino.