Hello James,
yes, I agree with you! Very difficult. Nomally PDE, but not usefull to handle. I think about the idea to calculate start and endframe of curves. Maybe it is possible to calculate it with approx. secants and a Lagrange Interpolation to get start-/end-tangent. I don't know how much work it is at the Moment and which precision we will get, but that can simplify the Problem alot. Another solution could be a simple Helix and flow it to circle - only if you really need a solution next time.

Array_along_path -sounds good!
Have a nice day
Karsten