> The first turn can be defined as always "right" or "left,"

No it can’t, not in 3D... it is just a turn.

You can however choose to rotate about the first segment until the turn is Right, then use this orientation for the rest.

In terms of normal form and restarts, who cares? Just generate the string both ways, it’s 2n computations, choose the lowest in lexicographic order, and life is good. If you get to billions of turns are humans really going to be doing the comparison? Surely we’d just stream the string into a hash function or something...