I started on the cabinet today, I removed all the hardware and the grille for cleaning and/or painting.
The grille cloth is in fair shape, there's one 1/4" hole in it, I could touch it up and it wouldn't be very noticeable but if someone makes a correct repro I may go with that.
Once it was removed I sprayed the grille with some strong cleaner, I wish I had a camera because what ran off that grille was really disgusting, it looked like strong black coffee going down the drain, I'm guessing it was Tobacco gunk.
It lightened up by several shades too, not quite as clean as the parts that were hidden under the trim but close enough.