We have calculated converged energies and tunneling splittings of the intramolecular stretching fundamentals and high-frequency, low-frequency combination levels of (HF)(2) on three potential energy surfaces. The resonance states are located against a broad background of continuum states by a moment-based stabilization method. The mean unsigned deviation from experiment for six tunneling splittings on the recently proposed S2 surface and on the BJKKL surface of Bunker et al. are 28% and 24%, respectively, as compared to 41% for the previously available results on the SQSBDE surface of Quack and Suhm. The results for the S2 surface are more accurate for excitation of the hydrogen-bond acceptor mode than for the hydrogen-bond donor mode, whereas those for the BJKKL surface are more accurate for the latter than the former.