Velux VCE Skylight and Blind Limit Setting

Greetings. I hope this is the correct sub-forum for this question. An interior doors to one of our bedroom has a gap between the door and the jamb. The house is old (116 y/o), the door is perfectly square but the jamb isn't, it is 1.75" off square. The door seals fine at the top but there is a diagonal line that starts at the top (lock side) and goes all the way down and basically you can see through inside when the door is closed (see pictures). The long black strip in the first pic is the dark hallway as can be seen from inside the room. The hinges side is perfect and the doors closes fine. The door's thickness is 1.5". We have some old identical doors up in the attic and my initial idea was to completely sand one of them and then cut it in the same shape of the opening. But then I thought about 'adding' some wood to the bad side, basically glue two pieces of 0.75" plywood, cut them to shape with a jigsaw, then glue/nail it to the door's profile to close that gap, re-send and re-paint the whole thing. I would appreciate any advise and opinion and of course any ideas for other fix solutions (other than a new door). One thing that I won't do is I will not remove the frame/jamb in order to straighten it. Way too much mess to do this in such a hold house with plaster and lath. Thank you.

I'm going to be replacing all of my interior doors as time and budget allows. I am considering getting a plunge router attachment for my Dremel to recess the area where the hinges attach to the door. Is this a good setup? I don't want to invest in a router, as I suspect it would sit on the shelf unused after this project. Is there a better method?