  The self-force program aims at accurately modeling relativistic two-body
systems with a small mass ratio (SMR). In the context of the effective-one-body
(EOB) framework, current results from this program can be used to determine the
effective metric components at linear order in the mass ratio, resumming
post-Newtonian (PN) dynamics around the test-particle limit in the process. It
was shown in [Akcay et al., Phys. Rev. D 86 (2012)] that, in the original
(standard) EOB gauge, the SMR contribution to the metric component
$g^\text{eff}_{tt}$ exhibits a coordinate singularity at the light-ring (LR)
radius. In this paper, we adopt a different gauge for the EOB dynamics and
obtain a Hamiltonian that is free of poles at the LR, with complete
circular-orbit information at linear order in the mass ratio and
non-circular-orbit and higher-order-in-mass-ratio terms up to 3PN order. We
confirm the absence of the LR-divergence in such an EOB Hamiltonian via
plunging trajectories through the LR radius. Moreover, we compare the binding
energies and inspiral waveforms of EOB models with SMR, PN and mixed SMR-3PN
information on a quasi-circular inspiral against numerical-relativity
predictions. We find good agreement between NR simulations and EOB models with
SMR-3PN information for both equal and unequal mass ratios. In particular, when
compared to EOB inspiral waveforms with only 3PN information, EOB Hamiltonians
with SMR-3PN information improves the modeling of binary systems with small
mass ratios $q \lesssim 1/3$, with a dephasing accumulated in $\sim$30
gravitational-wave (GW) cycles being of the order of few hundredths of a radian
up to 4 GW cycles before merger.
