@StellarFusion The "squirrely behavior" in your design and the reason you are receiving error messages about joint conflicts is that after your Ball37 joint your design is simply over constrained.
When trying to apply just one additional ball joint between the correct upper part and one of the free truss ends The joint solver simply cannot connect the two joint origins, because they don't precisely align. Precisely in this case far exceeds what you can measure with a caliper. You'd have to have a rester electron microscope to measure that. Or better. The precision needed is the internal precision of Fusion 360.
The root cause for that lack of precision are the fully undefined and imprecise sketches in the design.
That is also the one and the only reason why this works in the last two designs I posted. If you start with constrained and dimensions sketches it will work, otherwise it will not. There is really no other magic at work here.
Another thing that no one has mentioned here is that this design is a fully constrained, rigid design. As it pertains to Fusion 360 the ball joints are completely unnecessary to create this design. It can in fact be created with a single rigid group joint.