I would suggest for the stripping of the existing paint is to contact somebody local who can do CO2 bead blasting, as that will safely strip the existing coating off the unit, and not leave any residue either. I would also mask off the plate as well before taking it there, after stripping off all parts, and make sure to put sacrificial screws in all tapped holes, and mask off the entire area other than the areas to be blasted with some painters tape and card, using a firm grip tape so that the beads will not peel it, and at least 2 layers on the edge where it will be exposed to the beads, and probably not on the front face at all, but around the sides. A clean front with a coat of paint, hidden by the bezel is not going to be a concern.
I did the same for having heater plates recoated with a non stick coating by a local ship repair company years ago, helped though that the one guy was living next door to me in the flats at the time, and we got on well. Got a nice well blasted frosty plate back with a nice green non slip PTFE coat on it, emissivity definitely changes as you go from the oxidised rough matt aluminium extrusion to the PTFE, and it normally runs around 140C with 5 200W cylindrical heating elements in the body. Did have to do a lot of helicoil inserts though, but the existing holes were in any case well worn, the bead blasting with fine grit just finished off most of them rather well, but I was planning on doing the inserts anyway, had already ordered the inserts for the lot, simply as the stainless inserts survive heating cycles better.
Might take a spare one, with a PT100 pocket adaptor instead of the Fenwal thermoswitch, put in a PID controller and run it off 40VAC instead of mains ( slow down the ramp) and see about giving the flat face a coat of mystery emissivity Aerolac matt black as a poor man's black body, seeing as I do have a couple of them spare. Not going to win any beauty contests though for looks.