We present a model of ultra-high-energy cosmic ray (UHECR) production in the shock-accelerated fireball of a gamma-ray burst. In addition to the standard UHECR origin from neutron escape and decay into protons, our model considers direct proton emission through leakage from the edges of the accelerated baryon-loaded shells that make up the fireball. Depending on the optical thickness of the shells to photohadronic interactions, the source falls in one of three scenarios: the usual, optically thin source dominated by neutron escape, an optically thick source to neutron escape, or a "direct escape" scenario, where the main contribution to UHECRs comes from the leaked protons. The associated neutrino production will be different for each scenario, and we see that the standard "one neutrino per cosmic ray" assumption is valid only in the optically thin case, while more than one neutrino per cosmic ray is expected in the optically thick scenario. In addition, the extra direct escape component enhances the high-energy part of the UHECR flux, thus improving the agreement between the predictions and the observed flux.