Abstract Tidal disruption events (TDEs) are highly energetic phenomena that occur when a star is tidally disrupted by the central massive black hole in a galaxy. Fitting the observed X-ray spectra of TDEs with a first-principles, general-relativistic slim-disk model for the emission from the inner accretion disk can constrain the black hole mass M _• and dimensionless spin a _•. Multiepoch spectra can break degeneracies in parameter estimation, particularly when they include a period of super-Eddington mass accretion. Even one observed super-Eddington epoch can be useful. Constraints on {M _•, a _•} improve as a power law with the number of spectral counts; the power-law index is higher for a higher mass accretion rate. These results are supported by the successful modeling of real spectra in the nearby (0.0206 ≤ z ≤ 0.145) TDEs ASASSN-14li, 3XMM J150052.0+015452, and 3XMM J215022.4–055108, which were observed over multiple epochs with >1 ks exposure times. Guided by these results, we create an updated and expanded TDE catalog from the Open TDE compilation. We then explore the XMM-Newton and Chandra archives to identify 37 TDE candidates with promising spectra for constraining {M _•, a _•} with slim-disk model fits. At least seven TDEs are likely associated with intermediate-mass black holes. Three of the 24 TDEs with multiepoch UV/optical photometry from Swift have late-time observations that allow their light curves to be compared directly to model predictions from the X-ray spectral fits. Existing X-ray spectra for other TDEs can be augmented with future optical/UV data. Ultimately, our new TDE catalog will reveal the {M _•, a _•} distributions traced by TDEs, thereby discriminating among black hole growth scenarios and providing insights on general relativity and dark matter particle candidates. The new TDE catalog is here: https://github.com/aarongoldtooth/Census-of-TDE-and-Archival-X-Ray-UV-Data/blob/main/Full%20New%20TDE%20Catalog%20(Published).tsv, and the codes used to construct it are here: https://github.com/aarongoldtooth/Census-of-TDE-and-Archival-X-Ray-UV-Data.