Thanks for the replays and advice. I don't want to try to remove the upper and lower trim pieces, so it is tough to cut oversize, install, then trim a veneer piece. Working inside those 2 overlapping trim pieces has me gun shy to contact cementing a vineer piece even if it was precisely cut. I am pretty confident I can not repair at least 2 spots by light sanding
and re-staining. That's why I am leaning towards painting.