Is there any wiggle room in letting these too Inquisitor arches stack?
What are your RAW readings and what would you do in a home game?
I think RAW, they do not stack, as both alter their spellcasting feature. IMO I don't think it would be broken to allow it anyway, since the two archetype's alterations to spellcasting don't contradict each other. I'd allow it as a GM.
You could make the argument that since Ravener Hunter alters "the inquisitor's spells" and the Living Grimoire alters "orisons and spellcasting," they actually alter different features, but I think they are meant to be used interchangeably. For instance, like the Ravener Hunter the Deep Marshall magus also adds spells to their spell list while being restricted from certain spells but that "alters spellcasting" instead of "alters spells," while the Eldritch Scion magus changes to a Charisma-based spontaneous caster which "alters spells." I think altering spells vs spellcasting is interchangeable.
It looks like one alters spells, and the other alters spell casting. Is this one of those things where the archetypes were completed at different times and with different guidelines, and spells and spellcasting are actually the same feature?
I think so. They are used pretty much interchangeably from what I can tell in similar archetypes.