We report measurements of the positronium (Ps) interval in which atoms traveling in free space were irradiated with microwave radiation generated using a horn antenna. Previous measurements of this transition, performed using atoms in waveguides, exhibited asymmetric and shifted line shapes. In the free-space measurements we report here, much smaller line-shape asymmetry was observed, but with large frequency shifts that varied with the orientation of the horn antenna. Our observations are supported by line-shape simulations and demonstrate that variations in the microwave radiation field distribution can perturb measured line shapes and give rise to apparent frequency shifts without necessarily causing large asymmetries; this effect can explain previous measurements in which an apparent discrepancy with predictions from quantum electrodynamics was ob- served [L. Gurung, T. J. Babij, S. D. Hogan, and D. B. Cassidy, Phys. Rev. Lett. 125, 073002 (2020)0031-900710.1103/PhysRevLett.125.073002].