Alright, I'm quite embarassed now by this question.
I've been solving in linear velocity the whole time, not position. I think it got in my head that it was position since the algorithm iterates to converge on a position. Similarly, it wasn't obvious to me because it's "velocity"...
I'm working on an inverse kinematics problem (I make video games), and I'm reaching a bit beyond my education.
Right now, I've got an algorithm that solves the basic IK equation for a chain of rigid bodies connected by joints by approximately inverting ##J\Delta\theta = e##. Where ##\theta##...