The localization of a light particle (e.g., electron, positron, or positronium atom) in a fluid is known as self-trapping. In an earlier paper (B. N. Miller and T. L. Reese, Phys. Rev. A 39, 4735 (1989)) we showed that (1) the density-functional theories (DFT's) of self-trapping could be derived from a mesoscopic model that employs a quantum-mechanical description of the light particle and a classical description of the fluid, and (2) the application of scaling to the simplest variant of DFT results in a universal model for all fluids that obey the principle of corresponding states. In this paper we apply the fully scaled theory to the pickoff annihilation of orthopositronium. Predictions of three different versions of the theory are compared with the experimental measurements of McNutt and Sharma on ethane (J. Chem. Phys. 68, 130 (1978)) and Tuomisaari, Rytsola, and Hautojarvi on argon (Phys. Lett. 112A, 279 (1988)). Best agreement is obtained from a model that incorporates transitions between localized and extended states.