Mike,
I suppose anything is repairable. But, that being economically feasable is questionable in this case.

This, is a telling picture:



Bubba has attempted to drive out the face plate of the breech, and has damaged it badly. The two pins visible in the top of the face plate are ejector pins, and one is free floating at this point in time-it should be under spring tension when the breech is open, to push a fired cartridge off the extractor hook. The firing pin for the right barrel is not retracting, in fact, it is stuck in the hole. The other firing pin won't break a piece of masking tape placed over my snap caps, when the trigger is pulled.
I'm guessing that use with some sort of outsized load in punt gun fashion resulted in the fractures to the breech rails, and, Bubba, being Bubba, just worked them down with a file.
None of this damage looks recent, by the way.
There are better guns out there to begin a project with. I would advise anyone considering a Darne as a project to think twice about that. Unless, you live across the street from the factory.

Best,
Ted