Die Grinder. Carbide Burr. Vrooommm!
Cut the dish a bit sloppy is OK, a bit deep is OK...bed it in to the desired depth with 5200 and fair over the top of it...perfect job!
Alternatively, 4-1/2 or 5" cutoff disc in a hispeed-type body sander...lay the spinning edge against the opening and then sort of rotate the tool. Just...don't hang it up, and don't jump the tool. Watch your eyes...not OSHA-approved, but works just fine.
Dave