Very cool project!
I have a car in similar state with same problem.
Those quarters are Long and the Tail panel is still attached, there is some significant weight there acting on the quarters pulling them down. even if the support is off by only a 1/8 inch that would put a lot of twist into the panels and the body.
An Idea to check your quarter may be to install your Deck lid (Trunk Lid) to see if it sits square opens and closes????? That could also tell you when its level and supported enough?
This Type of work is normally performed on a Chassis Table but can be done on the floor.
a chassis table would make things much easier as you can temp weld in supports where ever you need them. to support the body here and there to get every thing leval and square.
You really are ahead of me the closest project I have to compare too is a 62 Studebaker,
I have the same problem My Quarters Sag as well. My Studebaker project sits waiting while other projects come first. I have some 12 inch I beam about 30 feet long I intend cut up to use to build a chassis table to build the car on.
I am gonna explain how I intend to do mine, It may be the wrong way to do it? I don't know? its just a plan in my head at this time! "Chopolds" would be better to give advice on all of this!!!!! He is a Great Fabricator and custom car builder with Fenominal fabrication skills!
First I intend to build a chassis table to build on.
Then I am going to center the body over the frame side to side and put the rake into the body I want over the Frame then fully support the body in that position level.
Then with the body fully supported over the chassis with the chassis fully supported centered and level then install the doors and the Trunk lid to make sure all is good Before any welding! Then triple check all Before welding the Body to chassis.
Wont do any good if the doors wont open and close or the Trunk lid doesn't sit Square or close. It will be hard to fix once the Chassis is welded to the body permanently.