I am going to refinish my kitchen cabinets by sanding & repainting them. The fronts have a 1/2" wide router-ed channel around the perimeter, about 2" in from the sides. Is there some way I can fill the channel so as to create a totally flat surfaced cabinet front?

Wood putty would be my choice. Apply enough to fill the channel & rise above the flat surface. It will shrink over 24 hours. It can then be sanded along with the rest of the wood to create a flat surface.

How wide/deep is this grove?

To wide and deep and a wood a basic wood filler could be a problem. Might have to go epoxy wood filler.

Epoxy is structural along with being a filler and it Won't shrink..

Considering the amount of work and the likelihood for a wavy surface you could consider buying new plain front panel doors. Kitchen cabinet doors, refacing and remodeling center..

How about router with a bit yourself to allow a piece of wood to be glued into new groove to allow a 1/2" X 1/4"? Or whatever strips of wood the putty, sand and paint.