Many key physical phenomena in JT gravity are only accessible if one goes beyond the topological expansion to capture non-perturbative effects. This can be done explicitly using random matrix models, if formulated in such a way as to extract non-perturbative physics. Such a framework, developed previously for JT by the Author, is briefly reviewed in this talk. Then a new tool is added: a particular Fredholm determinant. It allows for a surprisingly thorough excavation of the detailed microstate spectrum of a non-perturbative completion of JT gravity and several super JT variants. This then allows for the full quenched Free Energy to be computed for these models for the first time, completing the low temperature thermodynamics. Possible implications for the spectrum of higher dimensional near extremal black holes are suggested.