And very very quickly dumping that into SolidWorks:
We have an assembly!
And it can be mated together!
That highlights a problem with this method! The movement looks like balls. The flick at the top of the movement compared to the speed at the bottom is very much not what I want. I ran the in-tool motion animation feature, but it was animated too fast to identify the speed disparity. I will slow it was down and be more careful in the next test.