  We extend previous work concerning rest-frame partial-wave mixing in
Hamiltonian effective field theory to both elongated and moving systems, where
two particles are in a periodic elongated cube or have nonzero total momentum,
respectively. We also consider the combination of the two systems when
directions of the elongation and the moving momentum are aligned. This
extension should also be applicable in any Hamiltonian formalism. As a
demonstration, we analyze lattice QCD results for the spectrum of an isospin-2
$\pi\pi$ scattering system and determine the $s$, $d$, and $g$ partial-wave
scattering information. The inclusion of lattice simulation results from moving
frames significantly improves the uncertainty in the scattering information.
