I will go ahead and post this as it works well enough for my use case, though it feels like there's a better solution:
I was able to get the simulation to work if I drastically increased the scale of the whole model - so that even if what earlier felt like a large collision distance remained the same, it would still be relatively small compared to the path ...
Found the answer in this topic: How to prevent a cloth from entering another mesh?
Lowered the collision distance in both objects. Edit: And increased as much as needed the "impulse clamping" parameter.