Antihydrogen formation at AEgIS at CERN leverages charge exchange between Rydberg positronium (Ps*) and antiprotons, with cross-sections scaling with the Ps principal quantum number $n^4$ and inversely with relative velocity $𝑣^{−2}$. However, the motional Stark effect and velocity mismatch between Ps and antiprotons impose stringent constraints, limiting efficiency. Advances in transmission positronium
converters mitigate self-ionization losses and improve velocity alignment, promising a significant boost in antihydrogen yield. This work evaluates formation cross-sections, Ps velocity profiles, and the integration of advanced transmission Ps converters for precision gravitational studies.