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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 anarbitrary 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 thegyro-gravitomagnetic functions $(G_S,G_{S_*})$ is removed and (ii) to analternative gauge (called anti-$\rm DJS$ gauge, $\overline{\rm DJS}$) that ischosen so as to precisely reproduce the Hamiltonian of a spinning test-particleat linear order in the particle spin and keep the full dependence on the radialand angular momentum in $(G_S,G_{S_*})$. We use these results to extend by oneperturbative order, in PN sense, the analytical knowledge of the periastronadvance. After performing a suitable factorization and resummation of$(G_S,G_{S_*})$, the $\rm DJS$ and $\overline{\rm DJS}$ performances arecompared via various gauge-invariant quantities at the EOB last stable circularorbit. We eventually find some indications that the $\overline{\rm DJS}$ gaugemight be advantageous in the description of the inspiral dynamics ofcircularized binaries.

Gravitational spin-orbit coupling through the third-subleading post-Newtonian order: exploring spin-gauge flexibility