Since you are going regulated, the 'right' Vf isn't as important though the Js will probably last slightly longer on a charge.
As for tint, the W0s and X0s are the generally considered the whitest. I've done many TV1L DD builds for outdoors folks and all were pleased with them. The V1s tend to be slightly yellowish and sometimes slightly greenish. It's not horrible in actual use, esp outdoors, but if you compare a V1 to an W0 or an X0 on a white wall, the V1 is kinda ugly.
Also, on the Lux IIIs I haven't seen a huge range in tints with the V1s but with Q and R bins, I've seen some awful looking tints with the V1s.
Personally, I'd go for the TW0Ks though I'd prefer TW0Js.