So this may be useful to try understanding. The way I solve that problem seems very useful for your issue:
https://www.tech-artists.org/t/get-vertices-of-an-edge-loop-and-sort-them-around-their-unit-circle/14649/2
So here’s one way I’d approach this. It could ABSOLUTELY be optimized, but it’s a start.
First you need to know which way is “out” from your verts. Luckily, the vertices of a face in Maya are always counter-clockwise. So if you know the order of your joint verts, and you know the winding order of a face, you can figure out if a face is outside or inside your vertex loop.
So convert your vertex selection to a face selection, then for each face get its verts in-order, and figure out if that face is outside your ring.
Repeat that process to get all the rings in order.
Then, for every vert in your rings, grow a selection from it, and figure out which vert is in the next ring out.