Recent years have seen a rapid proliferation of the application of quantum scattering amplitude methods to the description of gravitational compact binary coalescence (CBC). After briefly introducing CBC and motivating the applicability of scattering amplitudes, I discuss the specific case of scattering Kerr black holes. Describing such scattering requires knowledge of the opposite-helicity Compton amplitude to all orders in spin. The correct amplitude is known up to fourth order in spin, while the Compton amplitude constructed from BCFW recursion on the Kerr three-point amplitude develops unphysical poles above fourth order in spin. I demonstrate the removal of these poles for all spin orders in the classical limit, without affecting the factorization properties of the amplitude. This produces a viable Compton amplitude which can deviate from the true Kerr amplitude only by contact terms. I analyze the contact terms that can be relevant for black hole scattering at 2PM, and fix a large portion of them by assuming low-spin properties of Kerr scattering hold to higher spin orders. Finally, this allows for a closed-form, all-spin expression of the 2PM amplitude between a spinning body (which may or may not be Kerr) and a Schwarzschild black hole.