After a decent amount of finagling I got the tetherball working. The rope even wraps around the post which was the best I could have hoped for.
The rope can’t handle extreme changes in velocity but for a simple solution it works quite nicely.
Using Jacob Fletcher’s Line Renderer script, here are the settings I used for my tether rope in Unity to get it working in VR (the scale is much smaller than the defaults):
As a side-note, I was so immersed that when I finished I turned around and put my controllers down ontop of a wall I had built in VR without realizing that there was no table there in real life! But I had placed a TV table there earlier and it happened to be at about the correct height. Talk about blending RL and VR!