- We study the propagation of ultra-high-energy cosmic rays (UHECR) in the Galaxy, concentrating on the energy range below the ankle in the spectrum at 4 EeV. A Monte-Carlo method, based on analytical solutions to the time-dependent diffusion problem, is used to account for intermittency by placing sources at random locations. Assuming a source population that scales with baryon mass density or star formation (e.g. long GRB), we derive constraints arising from intermittency and the observational limits on the composition and anisotropy. It is shown that the composition and anisotropy at 1e18 eV are difficult to reproduce and require that either a) the particle mean free path is much smaller than a gyroradius, implying the escape time is very long, b) the composition is heavier than suggested by recent Auger data, c) the ultrahigh-energy sub-ankle component is mostly extragalactic, or d) we are living in a rare lull in the ultrahigh-energy cosmic-ray production, and the current ultrahigh-energy cosmic-ray intensity is far below the Galactic time average. We therefore recommend a strong observational focus on determining the UHECR composition around 1e18 eV.