I know what the OP asked for, again it is moot because it's not possible. So it doesn't hurt to give alternative options without someone annoying chirping in to every suggestion I give.
I wonder how impossible it really is though? Like I mentioned earlier, you'd think with Nintendont able to be played with the Gamepad and Pro controllers at the same time, that it would be feasible to do the same with the Wii VC titles on the Wii U. I bet if the right person looked at the code and knew what they were doing, they could change how Wii VC titles and injects work on the Wii U to enable what we're talking about. One can hope, cuz while most of us are well aware of the alternatives already available, nothing will really be able to truly replace this ideal setup that theoretically could eventually exist.