Is the following assertion sufficiently unique to merit a paper? Every absolute conservation law implies a corresponding form of entanglement, not just spin (angular momentum). Linear momentum conservation would for example entangle originating equipment with wave packets and help determine packet dispersion rates. Mass-energy entanglement would provide a different way to look at wave function "collapse," via nominally instantaneous exclusion of finding the same mass-energy at remote locations. I have no idea what $T_3$ would be. Even some types of approximate laws may have corresponding entanglements.
No. The applicability of entanglement to all conserved quantities was covered in no less than the original EPR paper. @PeterShor answered my question, not me, but since he put it into a comment I'm adding this explicit answer to close out my own question. Peter, should you happen by, please feel free to copy your comment into an answer and I'll re-designate that as the real answer to give proper credit.