The Orbiting Astronomical Satellite for Investigating Stellar Systems (OASIS) is a 20-meter class proposed space terahertz observatory supported by an inflatable membrane architecture. To measure 150 mm and 1m models of the A1 reflective membrane antenna, two deflectometry configurations were designed. The smaller assembly and its corresponding deflectometer were simulated, built in our laboratory, and produce a reconstructable signal for clocked measurements of the highly-sloped pneumatic surface. We use non-sequential raytracing simulation to bound the maximum contributions of all shape errors and suggest the N-Rotations algorithm to remove the remaining radially asymmetric errors. Then, the 1m prototype assembly was tested inside a thermal vacuum chamber (TVAC). Differential deflectometry measurements tracked the 1m surface shape changes as it was subjected to a variety of environmental setpoints, cycled between three inflation gases, and also during controlled puncture. We summarize our development and results for absolute measurements as well as from TVAC testing.