The rapidity-dependent jet veto observables TBj and TCj provide a tight jet veto at central rapidity, gradually transitioning to a loose veto at forward rapidities. They divide the phase space into exclusive jet bins in a different way to the traditional jet veto observable pT j, and are advantageous to use under harsh pile-up conditions. We obtain predictions for the 0-jet gluon-fusion (ggF) Higgs cross section using both of these veto observables at NNLL′+NNLO, and compare these predictions to the prior state-of-the-art of NLL′+NLO. A significant reduction in perturbative uncertainty is observed going from NLL′+NLO to NNLL′+NNLO, with the NNLL′+NNLO predictions lying inside the uncertainty band of the NLL′+NLO predictions. We also investigate the relative sensitivities of ggF Higgs cross sections with TBj, TCj and pT j jet vetoes to underlying event and hadronisation effects using an NLO+parton shower calculation. We find that the cross sections with TBj and TCj vetoes have a reduced sensitivity to underlying event and hadronisation effects compared to that with a pT j veto.