I know your part wasn't related to fishing, just reminded me of the longline levelwinds I had to repair at times, figured yours was some textile part or wrapping machine.
Looks like it might be made from Delrin? if plastic?
Sorry I can't help with the toolpath as don't have 4th axis and never played with a wrap gadget.
But I would guess it would be done like a long pitch screw or actually 2 (left and right hand) with a segmented fluting toolpath
The math is beyond my abilities also
Anyway, it was interesting and I was bored, but would love to see the end results
Please post and with a snip of toolpath if possible