Understanding the proper formulation of AdS holography in two spacetime dimensions has led to fascinating progress in several directions. The main novel ingredient compared to higher dimensions is that the asymptotic behavior of the metric is only "nearly'' AdS in a certain precise sense. This difference allows for a very simple theory, Jackiw-Teitelboim gravity, to have a non-perturbative completion as a Hermitian matrix model. In this talk, we propose analogous modifications of the flat space boundary conditions in two dimensional dilaton gravity. These modifications allow a very simple theory, which we call Cangemi-Jackiw gravity, to have a non-perturbative completion as a random matrix model. We will discuss the Lorentzian and Euclidean formulations of this model, challenges in computing its non-perturbative scattering matrix, and which of its lessons are potentially applicable to four-dimensional celestial holography.