Supermassive black holes (BHs) have been observed to correlate with host galaxy bulge properties, leading to a fundamental open question in galaxy evolution: do BHs and galaxies grow in lockstep, or does the growth of one precede that of the other? We have uncovered a sample of local compact galaxies with uniformly old (≥10 Gyr) stellar populations and small radii (effective radii of 0.7-3.1 kpc) for their stellar masses [(0.5-3.8)x10^11 solar masses]. These galaxies are thought to be local analogs/relics of z~2 quiescent galaxies. Previous stellar-dynamical modeling of three galaxies in this sample found BHs that were over-massive compared to the BH mass - bulge luminosity relation, indicating BHs may build the majority of their mass before their host galaxies. Here, we present 0.14"-0.22" resolution Atacama Large Millimeter/submillimeter Array (ALMA) CO(2-1) data of the rotating circumnuclear disks in three other local compact galaxies. We fit gas-dynamical models directly to the ALMA data cubes, assuming the CO emission originates from a dynamically cold, thin disk, and we use the dynamic nested sampling code dynesty to determine Bayesian posteriors. Finally, we place these galaxies on the BH - host galaxy relationships. Making more dynamical BH mass measurements for the sample of local compact galaxies will significantly advance our understanding of BH - host galaxy co-evolution.