I managed to make the other, lower profile rings for the grills today, plus built the router table in which to make the recesses for the metal grilles. These fit much better by my eye. I used to have a much nicer router table, but it was liberated with the rest of my power tools some years ago.
This photo shows how far the thinned epoxy soaks into the MDF. This way, any subsequent sanding needed does not fuzz up the MDF. I'll also coat any bald areas where I did the machining. I can use 5 minute epoxy thinned with denatured alcohol for those parts, or any body work for any subsequent machining processes.
The epoxy is a good treatment for any screw holes after the fact as well. It hardens the holes so that the screw heads don't pull through it easily when tightening them. Another trick is, drill holes larger than needed for fasteners, fill the holes with epoxy putty, then predrill that for the actual threads to grab onto. I use fumed silica powder to make a sandable putty with epoxy, but talcum (baby) powder or even baking flour works a treat.