Environmental concerns have driven the development of alternative fuels and refrigerant working fluids with low global warming potential. Ammonia (NH3) is a potential zero-carbon fuel, while hydrofluorocarbons (HFCs) like R-32 and R-1234yf are being adopted as refrigerants. When mixed with air, these compounds can sustain slowly propagating flames with laminar flame speeds less than 10 cm/s. Unlike typical hydrocarbon-fueled flames, these slow flames are influenced by buoyancy-induced flow and radiation heat loss. In this study, we experimentally investigate the flame speeds of NH3/air mixtures using the constant-pressure spherically expanding flame method, while circumventing gravity-induced natural convection, and account for radiation-induced inward flow. To mitigate buoyant convection, a low-cost drop tower was built and used to study slow spherically expanding flames in free fall. A computational model (SRADIF) is utilized that combines thermodynamic equilibrium and finite rate optically thin limit radiation heat loss calculations to estimate the inward flow. The developed methodology is utilized to investigate slowly propagating NH3/air flames over a range of equivalence ratios. A systematic approach was undertaken to understand and quantify the errors that could arise when deriving the laminar flame speed. It was found that attempting to study slowly propagating flames in a static configuration, as opposed to in free fall, results in large differences in flame dynamics and subsequently all derived quantities. It is necessary to study slowly propagating flames in free-fall. Additionally, using experimental data that has not been corrected for radiation-induced flow leads to large errors in all derived quantities. Furthermore, direct comparisons of experimental measurements and detailed flame simulations are found to be necessary to determine if existing extrapolation approaches are applicable to these slowly propagating flames, which are challenging to study.