Although we haven't used it much in the last many years we still own a IH 5000 as a backup unit and it has the 19.5 header. So I had a look at the spring count and its 3 on the left hand side, 2 on the right hand side. I know through the years the springs would sag a bit and have to adjust them up to get the header light at the front corners of the header and noted that the left hand ones have very little adjustment left but the right hand ones have many many inches of adjustment remaining in them. That just goes to show how much more weight there is because of wobble box, drive shaft, reel drive all being on the left hand side.
Then I took note of where the top pin of the hydraulic cylinders are as there is three holes for pin placements along the side of the upper arm where the top end of the ram fits. The ram uses the rear most hole position on both sides of the swather, and the solid bar lifting rod linkage uses the very forward one on both arms. Then down at the bottom of the main arms that attach to and lift the header, the lifting rods on ether side of the swather use the forward hole.
What I wonder is if the rams and the lifting rods on your unit is set up properly or if someone took something apart and accidentally put ether the end of a ram or the lifting rod in the wrong position so its not mirroring the pin positions on the other lifting arm assembly. That would certainly throw everything out of whack.
Finally, if that all looks good, do a measurement from pin to pin of each ram to be sure they are the same length and that something isn't going funky inside the rams or the portion that slides on the top of the ram to allow for the table to float off its stop ( uneven ground, hitting a rock etc ) . So its just a guess that ether its a cylinder problem or another mechanical issue with that float type linkage if you will on the rams, maybe one is seized or spacers got put inside of it and it got cocked in there and won't let it settle back down. I looked in the operators manual and I find it odd that it doesn't show the same ram setup we have with that float system, perhaps someone else can shed more light on it as its been so many years since I touched those rams.