1950s house with door jamb built right into the masonry - what are my options?

I did almost exactly this on a '52 house I owned, same deal where the jamb legs were structural and the plaster died on the header the moment it got disturbed. Kept the jamb, hung a slab, and it's been fine for six years now.

The out-of-square fear is real but manageable. Old jambs almost never die in a perfect rectangle, so you don't square the door, you fit the door to the opening. Buy the slab oversized, scribe the hinge edge to match whatever lean the jamb has, and mortise the hinges to match the existing gains if you're reusing the same hinge locations. If the old hinges sat at a slightly different reveal top to bottom, just replicate that with the new door and it'll look and close right. Get a block plane and a cheap scribing compass if you don't own them, that's the whole trick. For the chewed up spot near the latch, wood filler will shrink and fall out eventually in a door that gets slammed. Cut the damage back to clean wood and glue in a Dutchman patch, a little scrap of matching hardwood shaped to fill the void, then sand it flush. On my door that spot was from years of the deadbolt tongue chewing the strike side, so check whether your latch or bolt is hitting the jamb and adjust the new door's fit accordingly.

New threshold is the part people rush. Get one sized for your slab thickness and the actual width of the opening, not what the big box store says is standard, and take your time getting the slope and height right relative to the swing. Seal the underside before it goes down.

Weatherstripping around the perimeter is where you make up for not having a factory-sealed prehung unit. A foam compression strip in the stop works fine if the stops are intact.

So yeah, your plan is reasonable. The contractor's 'smaller door inside the jamb' idea is the one I'd skip, that's how you end up with a weird narrow door forever.

Gonna disagree on the foam strip advice though. My '48 place has the same built-in jamb deal and the stops were so wavy that foam barely made contact in half the spots. What actualy worked was popping the stops off, flattening them with a plane, then running a V strip on the back side. Foam also cooks fast on a door that gets afternoon sun, I was replacing pieces every year untill I gave up on it. One other thing, dry-fit the slab and check it for bow or swell before you cut anything, because sometimes what looks like a wonky jamb is really just a door that came out of the wrap twisted.

Following this one because I've got the same setup at my place and haven't even worked up the nerve to pull the trim yet. Mine has that same thing where the wood frame goes right into the brick with no gap, so it freaks me out that everythign might be leaning on each other in there. Mine also has about five layers of paint on the frame, the oldest ones are probaly lead based so I'm just going to leave the paint alone and clean it up instead of sanding it. When you pulled your trim off, did any of the plaster crack on the sides too, or was it just bad up top?

Mine's the same setup and the thing that bit me was the old hinge screws. Sixty years of opening and closing had chewed the screw holes out so bad that the new door slowly sagged into the strike side no matter what I did. Stuffing the holes with toothpicks didn't hold. I ended up drilling out and gluing in hardwood dowels, then re-driving the screws into fresh wood. Snug ever since. Might be worth checking yours before you buy the slab, if the existing hinges wiggle at all you'll want to fix that first.