Addendum to "Relational Hamiltonian for group field theory"

In this addendum to E. Wilson-Ewing, [Phys. Rev. D 99, 086017 (2019)], we extend the construction of a Hamiltonian formalism to a new class of group field theory actions with a kinetic term that is local in the group variables and depends only on their derivatives; such a kinetic term will couple magnetic indices of opposite sign in the Peter-Weyl decomposition. The main results of that Wilson-Ewing paper for the resulting cosmology extend to this case.