We present a set of new generalized kinematic imbalance variables that can be measured in neutrino scattering. These variables extend previous measurements of kinematic imbalance on the transverse plane, and are more sensitive to modeling of nuclear effects. We demonstrate the enhanced power of these variables using simulation, and then use the MicroBooNE detector to measure them for the first time. We report flux-integrated single- and double-differential measurements of charged-current muon neutrino scattering on argon using a topolgy with one muon and one proton in the final state as a function of these novel kinematic imbalance variables. These measurements allow us to demonstrate that the treatment of charged current quasielastic interactions in GENIE version 2 is inadequate to describe data. Further, they reveal tensions with more modern generator predictions particularly in regions of phase space where final state interactions are important.