Reflection waveform inversion (RWI) updates the the P-wave velocity ($V_p$) macromodel beyond the depths sampled by diving waves, by exploiting wide scattering angle wavepaths in a reflective subsurface. Joint diving and reflection waveform inversion (JFWI) combines RWI and early-arrival waveform inversion (EWI), thereby constraining the shallow subsurface whilst enriching the low-wavenumber content of the deep $V_p$ model with reflections. In depth-domain $V_p$ inversion, ensuring consistency between reflectors positions and model kinematics comes at the cost of repeated least-square migrations, combined with carefully designed offset weighting. In order to efficiently address such co-dependency between reflective and kinematic parameters, we propose to cast JFWI in the pseudotime domain. As the velocity is updated, the reflectors are passively repositioned consistently with $V_p$, honoring the zerooffset two-way-time seismic invariant, and keeping the shortspread reflections in phase. By combining a pseudotime approach with a graph-space optimal transport (GSOT) objective function, we show that it's possible to reconstruct a complex velocity macromodel from short offset 2D reflection data containing surface-related multiples and ghosts, starting from a 1D initial guess; compared to a depth-domain inversion, the computing cost is reduced of one order of magnitude, associated with a significant saving in man-time, thanks to a simpler design of data weighting and inversion strategy.