These shots with indoor and mixed lighting where I can't use a flash are difficult. I think WB does matter a great deal, especially if it adds a cast to a shadow that you can't get rid of. I don't think you can ignore that. Fortunately I was able to test both the 1DX and 5D3 in these harsh conditions and they performed similarly.
You know, you can always develop the RAW twice, once for each white balance, and then composite the one into the other using a mask and a big soft brush....
You know, you are absolutely right. I forgot PS can do that.
I am also going to do some test shots downstairs this evening with tungsten and fluorescent lighting, and "meter" my WB reading off a styrofoam cup. Secondly, I'll apply a flash on a second series of photos. Funny how when you are so used to shooting in one environment you really don't appreciate the difficulties of other environments.