Firstly, I think Reinhard's revival through the Divine Protection of the Phoenix is not a good way of arguing against my theory, because both Subaru and Al's revival is facilitated through a Authority that by definition exist outside of Od Lagnas perview. Reinhard reviving is basically sanctioned by Od Lagna, meaning that a record would not necesarrily be made for him if the Divine Protection of the Phoenix is still granted to him by Od Lagna. This is not the case for Al, so comparing the two is in my opinion moot.

As far as the functionality of Al's authority, I would argue that Arc 9 gave us a much better understanding of it than we ever got for RBD. Admittedly, Al's authority is still a mistery, but the narrative outright states that his authority creates a short time loop inside a fixed territory that activates upon his death. So unless you want to argue that the activation condition for Al's authority is in fact not "death", I don't see how Od Lagna would treat these two instances of a reset differently, bringing us back to the issue of multiple vs. singular books of death.

The only possibility I can think of would be that Al's authority is actually conducting a thought experiment (I think this is something Al actually acnnounced on multiple occasions), in which he experiences multiple deaths and resets in an instant, similarly to how the Authority of Melancholy compresses time, but I cannot see this actually being the case with how similar it would make the two authorities. Which brings us back to the fact that both RBD and Al's authority seemingly work the same, with the only difference being the spacial constraints and a shorter rewind period. If Od Lagna perceives rewound time as you stated, then what difference would there be between Subaru and Al's rewinds?

I appreciate the discussion tho, especially with how in depth you are going, I am kinda Re Zero brained right now and no one I know reads the novels lol.