  Finite-volume pionless effective field theory (FVEFT$_{ \pi\!/ }$) at
next-to-leading order (NLO) is used to analyze the two-nucleon lattice QCD
spectrum of Ref.~\cite{Amarasinghe:2021lqa}, performed at quark masses
corresponding to a pion mass of approximately $800 $ MeV. Specifically, the
effective theory is formulated in finite volume, and variational sets of wave
functions are optimized using differential programming. Using these wave
functions projected to the appropriate finite-volume symmetry group,
variational bounds from FVEFT$_{\pi\!/ }$ are obtained for the ground state, as
well as excited states. By comparison with the lattice QCD GEVP spectrum,
different low energy constants (LECs) are constrained. Relativistic corrections
are incorporated, allowing for the extractions of NLO LECs, as well as the
leading $s$-$d$-wave mixing term in the deuteron channel.
