  We examine the Regge limit of holographic 4-point correlation functions in
AdS$_3\times S^3$ involving two heavy and two light operators. In this
kinematic regime such correlators can be reconstructed from the bulk phase
shift accumulated by the light probe as it traverses the geometry dual to the
heavy operator. We work perturbatively -- but to arbitrary orders -- in the
ratio of the heavy operator's conformal dimension to the dual CFT${}_2$'s
central charge, thus going beyond the low order results of arXiv:1812.03120 and
arXiv:2007.12118. In doing so, we derive all-order relations between the bulk
phase shift and the Regge limit OPE data of a class of heavy-light multi-trace
operators exchanged in the cross-channel. Furthermore, we analyse two examples
for which the relevant 4-point correlators are known explicitly to all orders:
firstly the case of heavy operators dual to AdS${}_3$ conical defect geometries
and secondly the case of non-trivial smooth geometries representing microstates
of the two-charge D1-D5 black hole.
