The detection efficiency for large area alpha sources with adjustable heights of a raised lip around the edge were measured by 2π gas-filled proportional counter. The variations in low-energy spectral shape were modeled using a Geant4 radiation and charge transport Monte Carlo simulation, to enable extrapolation of the spectrum to zero energy. COMSOL Multiphysics finite-element analysis was used to explore changes in the spectrum gain in the presence of a lip. It qualitatively reproduced an increase in peak height due to an increasing height of the source lip. A spectrum analysis procedure was developed to perform integral counting on sources with a lip. The experimental results were used to validate the model, which was then used to predict the changes in 2 π counting efficiency for other source-lip geometries.