Laminate the top
I once worked in a millwork shop and saw similar mistakes fixed by letting in what they called a "Dutchman". It involved enlarging the hole to a regular size, cutting a patch from similar material, and then gluing it into place. In your case MDF is hard to glue as it swells with normal wood glues, but poly glues (Gorilla glue is the brand that comes to mind) seem to work. Once done, I would cover the whole top with plastic laminate and they re-route the insert hole using a template. Laminate makes a great top, it is slick, cleans easily, and is forgiving of glue and paint mistakes.
Big routers are no fun to hand hold, I have lots of stories from my millwork days!