The computational design of molecular quantum devices requires methods that capture "the quantum and the chemistry," approaching chemical accuracy for large numbers of entangled and/or strongly correlated electrons. Projected-interacting full configuration interaction (PiFCI) is a candidate for such simulations, providing a formally exact and systematically improvable approximation for correlation in large active spaces. PiFCI extends Kohn-Sham density functional theory by introducing multiple reference systems, each experiencing an electron-electron interaction projected onto one or more one-electron states. Compact CI expansions yield near-exact reference system wavefunctions, and projected exchange-correlation (XC) density functionals enable formally exact combinations of reference system correlation energies. This work presents a general treatment of the projected interactions in PiFCI and introduces regularized second-order many-body perturbation theory (MP2) as an approximate projected XC functional. Numerical results show that PiFCI plus regularized MP2 can accurately treat dynamical and nondynamical correlation in relatively large active spaces, including stacks of entangled singlet-coupled tetrathiafulvalene and phenalenyl organic radicals modeling molecular quantum devices.