Lattice QCD studies of few-nucleon systems can provide a bridge between the Standard Model of particle physics and effective theories of nuclei. Calculations of nucleon-nucleon interactions, as well as nuclear matrix elements of electroweak and beyond-Standard-Model currents, can be used to inform nuclear effective theories whose predictions are relevant for a wide range of experiments searching for new physics using nuclei as targets. I will discuss a recent variational study that explores two-nucleon systems with unphysically heavy quark masses using a wide range of operators, including compact six-quark operators and products of plane-wave nucleons. The results provide robust upper bounds on two-nucleon energy spectra and highlight the importance of systematic uncertainties arising from excited-state effects in lattice QCD calculations of few-nucleon systems.