You say, “My theory is that the floor has sagged and thing are a bit off kilter”. And later you state that, “there are no load-bearing walls involved”. But yet there is a door frame that is out of square.
My concern is that you might not know where all the load is being transfered to. There was, after all, a steal support column that was there for some purpose or another. I am not saying that you aren’t right, just that it is my concern that there is a chance you may not be.
If the beam is not butted together above the old support, not bearing any load other than the floor, and this is a simple sagging problem, then you can pretty much jack it up anyway you want.
Got any pictures or blueprints to share?