On the D70 it is possible because of a much weaker IR rejection filter, the WB has little to do with these wavelengths. Regardless, they aren't getting to the sensor so the WB adjustment has nothing to work with.
Maybe the automatic WB may not help, but on the D70s I usually do a manual pre-set for the WB by pointing the camera to a green part of the frame, with the Hoya R72 filter on, and then recompose the photo to get great results.(That is, with my D70s that was not transformed for IR).
I don't understand your problem with WB though. Shoot in RAW and you can change the WB to whatever you like in PP.
Not all PP programs allow you to go down to the WB settings of IR, and also they are not tailored to do it, the best is to use a green grass with the filter on. This is like using a gray card on a regular photo. Note: I use RAW for IR photography, this allows additional tweaks in PP.
Many people get a dedicated D70 and have the in body filter replaced. so you dont need a filter out front and it will work with all your lenses. I have been thinking of doing that. but I love my 1/8000 flash sync on my D70 so may be I will need to get a second one :-)
I'm in the same boat as you :)
The D7Ts is a great camera, I have it alsmost from the date it came out from the market, love it.. but after 50K photos, I better start looking for a new one. (That is the reason I want to migrate to the D7K and keep the old one as backup. I will miss the IR capabilities on the new one.