Item 2 More details on the motor. You have a great deal of expertise on motors. I am just an average mechanic. If I were there, I would take the motor back to the shop that wound it and say, "put this on your bench, figure out how the wires should be hooked up to connect like this diagram says and make it draw the correct current and run the correct speed. If they have to rewind it again, so be it. They could also figure out the correct capacitance to connect with each winding." Get it right on the bench before playing in the field. There is a company in Chicago that specializes in old Otis equipment. If you had to start with a different stator and rotor, that might not be the worst thing. You are spending a lot of time and resources and don't seem to be gaining ground.

Item 3. 3.1 Good job. How much experience does this full Service Company have if they can't fix this simple problem??? 3.2 See 3.1, Did you notice the SOS switch. Did you incorporate that switch in that grouping??? 3.3 You need both sets of contacts to be used on this elevator. If not, either you won't have ANY doorlocks or after the first trip into the floor and unlocking the doors, you won't be able to leave the floor. 3.4 see 3.3.
3.5 CLOSED and LOCKED are two different things. Opening the door may stop the elevator, but it does not insure that the doors are locked.

Item 4. The OR circuit is only in effect for 3" above or below the floor. As soon as you run off the limit switch, one of the circuits are open and running depends on the other circuit. Any elevator parts house--Adams, SEES, Quality, etc. can provide a freight emergency keybox to allow the doors to be opened by a competent mechanic.

Item 5. The limit switches shown in your pictures are not of the vintage of this elevator. As long as the current rating is okay, they should be fine. The diagrams did not show the size of the control fuses, but I am fairly sure those contacts should do the job. The reason for a final limit switch at BOTH ends of the hoistway is so that the machine doesn't continue to run and either damage the cables or set fire to the building, or sever the cables if they run long enough. All of these things have happened.

Looking at your scope diagrams, it seems that your brake is not adjusted properly. Could be that there is still a problem with the motor (likely), but I see excessive current possibly brake not picking fast enough or stroke too long, oor cores too far apart. Regardless of motor, empty car up should not be a heavy draw. Have you balanced the car?? What percentage did you use?? 40 to 43 is standard for geared cars.

It looks like you are trying to do them a great job. Where is this project located???