I wouldn't use liner as a solution, especially around door hinges.
My theory is the movement of the hinges could cause cracks in the liner then you'd be trapping moister in and never see the rust until it's too late.
If it were me, I'd prep it really well and lay a couple of extra coats around those areas to help prevent it.
My plan is to have them fully prepped and primed first so I'm thinking all metal will be covered. We're doing the same treatment on the door where the parts meet. Hopefully that does it.
I can't just buy hinges at this point because the doors have bubbling paint too. It moved faster than I thought.