My synonym finder has "fork, bifurcation, corner, angle, bend, divarication, division, groin" as synonyms for crotch - any of those more pleasant to the ear and, which is more to the point, is more descriptive and clear? Open loop has a problem when looking at the OP and I suspect that may be part of the problem. Look back at the OP and you will see that it is intended these words be descriptors of direction rather than just shape, with clarity of shape added by way of vectors or angles. We are trying to set up, not the framework for words we are already familiar with and confused by, but words that have clarity for us and for others so that we may have a more specific distinction on what we do - action words. Bight does not have that distinction. Curve may be described by degree of arc, by radians, by vector position and so on. It is distinctly different than a straight line, which is taken by some to include a bight (cf. ABOK). As for the apparent prurience associated with the word crotch, one should really go beyond to look at definition #2 in the dictionary "a fork in a tree, road or river" which may mean that "fork" has some merit, although I must admit to thinking of multiple tines when I think of the word fork, as in dessert fork.
SR