If I ever run across these problems on site and I can't just run away I cut a fairly large hole in the wall and put a long piece of pine in. The technique is proprietary! It mostly involves swearing and sweat.
Tying the bit of wood to some string helps pull it tight when putting your first screw back in and helps you avoid dropping the wood into the cavity. Been there many many times!
I can only find one, I think the other is obscured by the door frame.