So I messed around with this last night and came up with a temporary solution. I think the latest patch allows you to have both HDMI and Component (A/V) cables connected at the same time. In my case I am connecting this to a projector. If you have an Optoma HD20 it has Component IN on the back. When you play Wii U games, change the 'Display Settings' in the Wii U menu to HDMI. When you want to pay Wii games change the 'Display Settings' to 'Other' or 'Component' (I can't remember what it actually calls it). You shouldn't have to move any cables around. The Wii games wont look quite as good because you're using Component, but at least you will be able to play them for now. Hopefully we'll see a fix for this in the near future.
Also you'll need a long Component cable, I believe I got mine from Monoprice for around $15 (25')