There's so much out there about refinishing/repainting kitchen cabinets, but I haven't found anything addressing what I will call "veneer inserts." My kitchen cabinet frames are solid wood (oak, I think), but the cabinet face is a veneer. (I'm not 100% positive that the material is veneer, but it's extremely thin and has a plastic feel.) This "veneer insert" is held in place by a groove in the surrounding cabinet frame. The groove is just off center of the wood frame. (I believe this is/was a fairly common builder's grade cabinet.) I've attached a few pictures if that will help visualize my cabinets.

What I'd like to do is either pain the veneer, or even better, replace it with something else. For example, maybe I could use a glass front, or possibly replace the current veneer insert with a darker/nicer looking veneer. Does anyone know how one would go about doing this?

My concern with cutting out the veneer that's in there right now is that I suspect it will leave a very noticeable groove in the cabinet frame.