the only way i could avoid the deformation you mentioned was to take my twisted pairs - I could not get it to work with 3 pairs as it is a rectangular shape but 2 pairs was fine - and create a lattice deformer on them. Because the lattice acts as the outerbound if you apply a twist deformer to the lattice then you seem to get proper twisting.

I hope that helps a little better, as for 3 pair well you're going to have to get creative on that one haha.

-Cheers
-Alexander