Theories of gravity that obey the weak equivalence principle have the same parametrized post-Newtonian parameter gamma for all particles at all energies. The large Shapiro time delays of extragalactic sources allow us to put tight constraints on differences in gamma between photons of different frequencies from spectral lag data, since a nonzero Delta gamma would result in a frequency-dependent arrival time. The majority of previous constraints have assumed that the Shapiro time delay is dominated by a few local massive objects, although this is a poor approximation for distant sources. In this work we consider the cosmological context of these sources by developing a source-by-source, Monte Carlo-based forward model for the Shapiro time delays by combining constrained realizations of the local density field using the Bayesian origin reconstruction from galaxies algorithm with unconstrained large-scale modes. Propagating uncertainties in the density field reconstruction and marginalizing over an empirical model describing other contributions to the time delay, we use spectral lag data of gamma ray bursts from the BATSE satellite to constrain Delta gamma < 2.1 x 10(-15) at 1 sigma confidence between photon energies of 25 keV and 325 keV.