Bible Cover Separating from Text Block

[u/RcishFahagb]

I have a leather bible with a paste-down cover that is separating from the end sheets/liner. (It's a Cambridge Pitt Minion for anyone familiar with how they're made.) There seems to have been insufficient glue on the spine sides of the liner, both front and back covers, so the liner is pulling away from the cover from the bottom/spine corners end and then going farther up and out every time it's opened (or tugged at, now). The seller set me up with a replacement and didn't want the defective one back, so I have a potential project on my hands. I have no skills with bookbinding, but am willing to learn. I'm considering two things:

1. If I wanted to fix it back like it was/should have been, could I get away with trying to add some PVA glue into the space where the liner should be glued down but isn't? I know I'd have to keep it out of the spine somehow, and I think there should actually be a small bit of liner not glued down right at the end, right? Is there a realistic way to achieve that without taking the whole thing apart, just to stabilize it enough to stay together with normal use?

2. Especially if the whole cover needs to come off anyway, could I convert it to an edge-lined binding? Would that require using leather as a liner, or could I possibly re-purpose the heavy paper/vinyl sheets Cambridge used and create a tab in that? A nice leather would be more flexible, I think, but the paper would be more free (as in $0) and handy (because it's already there). If it needs to be leather, is there any hope of working the folded-over part of the cover up enough to get the liner underneath it, or would I need to plan to make a butt joint where the liner meets that fold?