We investigate a high-z cosmological model to compute the co-moving sound horizon r s at baryon-velocity freeze-out towards the end of hydrogen recombination. This model assumes a replacement of the conventional CMB photon gas by deconfining SU(2) Yang-Mills thermodynamics, three flavours of massless neutrinos (N ν = 3), and a purely baryonic matter sector (no cold dark-matter (CDM)). The according SU(2) temperature-redshift relation of the CMB is contrasted with recent measurements appealing to the thermal Sunyaev-Zel'dovich effect and CMB-photon absorption by molecular rotations bands or atomic hyperfine levels. Relying on a realistic simulation of the ionization history throughout recombination, we obtain z * = 1693.55 ± 6.98 and z drag = 1812.66 ± 7.01. Due to considerable widths of the visibility functions in the solutions to the associated Boltzmann hierarchy and Euler equation we conclude that z * and z drag over-estimate the redshifts for the respective photon and baryonvelocity freeze-out. Realistic decoupling values turn out to be z lf, * = 1554.89±5.18 and z lf,drag = 1659.30 ± 5.48. With r s (z lf,drag ) = (137.19 ± 0.45) Mpc and the essentially model independent extraction of r s · H 0 = const from low-z data in arXiv:1607.05617 we obtain a good match with the value H 0 = (73.24 ± 1.74) km s −1 Mpc −1 extracted in arXiv:1604.01424 by appealing to Cepheid calibrated SNe Ia, new parallax measurements, stronger constraints on the Hubble flow, and a refined computation of distance to NGC4258 from maser data. We briefly comment on a possible interpolation of our high-z model, invoking percolated and unpercolated U(1) topological solitons of a Planck-scale axion field, to the phenomenologically successful low-z ΛCDM cosmology.