I don't have TWs so I can't say my opinions are 100% truth, but as far as off roading with re-treads goes, TWs own site says not to air their re-treads down. I'm sure that's because the tread can separate from the rest of the tire when it has low pressure and the rubber is being pulled, smashed, folded, etc.. against rocks and other obstacles. Re-treads also ring my common sense alarm...
Ever seen a nice, perfect strip of tire tread just laying on the freeway? Yup, that's what re-treads can do - especially on hot days. Now I don't know if that's common with TWs in particular, but I'll stick to normal tires personally.