A couple of screwdrivers and a hinged mirror were all I needed to remove the glove box lock
Close up of the glove box lock hole
Once I got the door and glove box locks out I took them to a local locksmith, who kept them for 3 days before telling me they couldn't fix them. It looked like I needed a specialist, so I turned (as I always do in cases like this) to Hemmings_Motor_News, the largest and best publication for everything related to the old car hobby. I found a locksmith, Jessers, who specializes in classic cars. They said they could do my lock cylinders, so I sent them away.
Door locks (left) and glove box lock (right)
I waited a little over a week before getting them back. I was surprised to find that they had not rebuilt the glove box cylinder (they never called me to inform me of this, just put a note in with the other keys). I later spoke with them and they said they could make a new key for the lock. This was after I had already received the locks though, so I decided not to bother with it: it's not the end of the world if I can't lock my glove box.
The day after I received the locks I installed them in the car. I had to remove the door handles to do it, which is also a simple operation, accessible through a hole in the door jamb. The most difficult part was guiding the rebuilt lock cylinders back into their proper slot in the door. As you can see there is a long shaft protruding from the cylinder, which needs to line up exactly into a slot on the opposite side of the door, which you can't see because as you put it in, the lock cylinder blocks your view. I slipped a magnetic_grabber in through the handle hole to guide the shaft into the slot and it worked well.
Lock and handle removed. I went through the handle hole to guide the locks back in. Note the original Stardust Ivory color (too dirty here too look very good).
Lock now installed