You are right, Dustin. The next step would be to request reconsideration by the full court at the 10th Circuit. That normally does not happen unless there was an obvious flaw or conflict with existing binding precedent. Beyond that, the only recourse is the U.S. Supreme Court.
The SC could grant certiorari to resolve a split between various circuits. However, that is itself a long shot. One problem is that the question has no bright line, but revolves around a matter of degree. When do registry requirements become so onerous that it tips the scale to legally constitute punishment? Three turns verses two turns of the thumb screws?
Somebody had the idea that a wife or child could raise a lawsuit based on tangible collateral harm. That might be a workable approach if one could get past the question of standing. They would also be afforded more sympathy. This needs to be a worst-case situation. We need to find a family in a very oppressive state–like Florida– that became homeless due to the father’s registration causing a loss of income and/or due to residency restrictions. Also it is best if the registrant is on the registry for some “minor” sex crime long ago. I would contribute what I could to that legal approach.