The observation of Pauli blocking of atomic spontaneous decay via direct measurements of the atomic population requires the use of long-lived atomic gases where quantum statistics, atom recoil and cooperative radiative processes are all relevant. We develop a theoretical framework capable of simultaneously accounting for all these effects in a regime where prior theoretical approaches based on semi-classical non-interacting or interacting frozen atom approximations fail. We apply it to atoms in a single 2D pancake or arrays of pancakes featuring an effective A level structure (one excited and two degenerate ground states). We identify a parameter window in which a factor of two extension in the atomic lifetime clearly attributable to Pauli blocking should be experimentally observable in deeply degenerate gases with~103 atoms. Our predictions are supported by observation of a number-dependent excited state decay rate on the 1S0 - 3P1 transition in 87Sr atoms.