Thanks for the reply, Cerbera!
I looked into those things and turning the banking off has helped the spinning, so thanks for that!!! I have tried the other things you have said and, yes, it has lessened that energy being imparted to it (for want of a better way of putting it) but not eradicated it - like you said.
I have tried another setup, where I use connector tags with the rope simulation instead of rope belts. In this scenario, the problem is exacerbated which is both a good thing and a bad thing. Bad, in that it's still a similar issue, but good in that in seems to be pointing to the problem... even if I can't understand the solution. As you can see, in the attached scene file, the drawn connections are 'pulling' just at the first frame (sending a shockwave through the rope spline).
This seems to be pointing to something having an effect on the dynamics, but I just can't figure out what...
StringTest_V3.c4d