  We build upon recent work by Antonelli et al. [Phys. Rev. Lett. 125 (2020) 1,
011103] to obtain, within the effective-one-body (EOB) formalism, and for an
arbitrary choice of gauge, the third-subleading post-Newtonian (4.5PN)
corrections to the spin-orbit conservative dynamics of spin-aligned binaries.
This is then specialized to: (i) the well-known Damour-Jaranowski-Sch\"afer
($\rm DJS$) gauge, where the dependence on the angular momentum of the
gyro-gravitomagnetic functions $(G_S,G_{S_*})$ is removed and (ii) to an
alternative gauge (called anti-$\rm DJS$ gauge, $\overline{\rm DJS}$) that is
chosen so as to precisely reproduce the Hamiltonian of a spinning test-particle
at linear order in the particle spin and keep the full dependence on the radial
and angular momentum in $(G_S,G_{S_*})$. We use these results to extend by one
perturbative order, in PN sense, the analytical knowledge of the periastron
advance. After performing a suitable factorization and resummation of
$(G_S,G_{S_*})$, the $\rm DJS$ and $\overline{\rm DJS}$ performances are
compared via various gauge-invariant quantities at the EOB last stable circular
orbit. We eventually find some indications that the $\overline{\rm DJS}$ gauge
might be advantageous in the description of the inspiral dynamics of
circularized binaries.
