I think someone in the past posted calculations (in relation to general vertical and horizontal tailstock alignment) that showed the horizontalness of the boring head is not super critical, so just ordinary care is needed to put it into the tailstock for an acceptable result.
Something to assist this might be a block that goes between the top slide and the flat on the head.
If length were an issue, the Morse arbor on the boring head could be removed and an adaptor that clamps it to the OD of the tailstock barrel be made. That might incorporate a key, to interface with the keyway on the barrel.