The issue is that the 7a (aka "mode D") invitatory psalm is recited on the final of the piece (I/ Populus Domini, ending on Ré, being considered as 7th mode transposed even though its modality is archaic/unclear), so employing it here with recitation on Ré and not on Sol would be modally incorrect (but melodically unproblematic...) - to be continued. Or perhaps the 7a tone is very much 7th mode, and the I/ Populus Domini is simply out of place.

Sandhofe's melody was checked against a number of diastematic sources. There are variants (French variant e.g. https://gallica.bnf.fr/ark:/12148/btv1b6000531z/f147.item has a torculus on (vigilan)TI(bus) and the classic 7th mode French formula on (domi)NUS (sol/la-do-sol/la-sol/sol-fa instead of sol-sol-fa) ) but globally, Sandhofe's melody is the best restitution that fits H.

NABC addivi