You know, from what you have told me, and in my opinion only, I would leave it as it is.
you know my Grandparents lived in Missouri until their death and they had a home very similar to what you described as yours. The joists seen from the basement had to be 2 x 12 or something like that and they were solid also. I always remember as a kid playing down there and I always remember this set of permanent adjustable floor jacks in the center of the basement. They were the kind that you inserted a metal pole and turned the screw and thus the jack became higher. They also had a sag and he used this jack system NOT to become level again, but to STOP all further sagging.
For you to become full bubble again, you will move allot of stuff, walls, plumbing, electrical cords, you name it. the new drywall will surely be affected.
There will be other comments on this I am sure, but my own is to leave it alone and just try to stop the movement any more. Maybe it has stopped on itself anyway.
You can determine a few spots on the first floor for a base line. Place a level, a long one, on that spot and measure it once and write down that measurement and then do it once a month or so. See where you go.
remember, a rule of thumb is that it will close up during the rainy season and cold weather and open up during the hot summer.