So, what’s changing is not what the modifier attaches to, but the modifier itself. As far as I can tell, that doesn’t affect the MRSs, except for getting rid of the quantifier in cases where the modifier is a NOM. But the rest seems to work.
That said, the motivating example for including this switch was the construction in Ancient Greek where you get something like “the [the cat’s] paw” – that is, cases where the modifier is an NP. I am not quickly finding any examples of the modifier being a NOM – a lot of the examples I have of modifier-like possessives come from languages where only pronouns can act as modifier-like possessives (like Italian) so the NP/NOM distinction isn’t relevant. Perhaps it’s worth sending a request to lingtyp to see if this happens before trying to accommodate it?