The problem lies in the offset of the AV port that goes into the WiiU overlaps with the HDMI port, preventing you from plugging in both at the same time. If the orientation was opposite, it would protrude toward the power port on the back of the WiiU (probably blocking it), but it would give more clearance toward the HDMI port. You could just use the converter's HDMI port, which... is not ideal, but I guess that would work. I think I will try it to see what resolution it puts out. Stinks that it will go from analog to digital though.
Now, if you had a super slim connector type of HDMI cable, I suppose you could beat the spacing conflict, but it literally almost overlaps.
I wonder if I should just chisel/Dremel away at the housing of the HDMI converter. I might, after seeing the signal converted. Will let you know.
Update: I tested it and the AV video output works, as if it was for the Wii. It's at 1080p but doesn't look nearly as crisp as the WiiU's HDMI out. I'm gonna crack it open or take a Dremel to it and see if i can use both.
Update again: Idk if you're as invested in this as I am now, but I think there is hope in Dremeling the Wii2HDMI! Look at this circuit board:
https://gbatemp.net/attachments/dsc01794-jpg.218945/
There's like nothing there in that area right were we need clearance! Not sure if I will open it up or just hack away from the outside in, little by little. I really don't like the Wii2HDMI video quality. Otherwise, if you happen to have a Monoprice Ultra Slim HDMI cable, you might have more luck (or require less Dremeling)