VEY good answer Razor, man you are batting 1000 today!

2 more ways to try:

Spline IK, kinda messy, but it worked for me for a rope sim.

and

A Simple softbody curve with the exact method you used with point constraigning rigid body objects, however, add more of them to make it look like one of those old plastic segmented jump ropes the kids have.

Then turn on collisions for the cubes, and in theory, nothing should intersect.

Play with it and get back to us!