The only ways I know is:
1 - rotate the file 180° so that the heaviest coverage is at the lead edge and the lightest coverage is at the tail
2 - use a heavier weight paper.
3 - check for excessive impression/blanket squeeze which may be stretching the paper.
I don't think you can employ any file distortion in prepress to solve this. Maybe others folks have more ideas. Sorry.
In 1997, one of the two tech papers I presented at the TAGA conference was related to web tensions and repeat length in web offset presses. It was an engineering paper with equations related to the main factors affecting repeat length and this is also very closely related to print length. In the paper both web and sheetfed conditions were discussed. This paper was written from investigations I did in the mid 1980's at TetraPak Canada, where one of the critical issues was insetting, which is the process of printing to a predetermined repeat length.
Anyhow, one of the interesting factors was blanket squeeze and shear forces in the nip. As you suggest, this might distort the paper, but squeeze on its own will affect the pulling rate of the blanket on the paper being printed. Shear forces will also have an affect. In the tech paper, these factors were provided in a model (equations) which was based on careful measurements from testing.
Sheetfed is a more difficult problem to obtain predictable answers to these issues due to the fact that with a web press, the web itself provides some stability that an unfixed sheet can not.
Around 2001, I was working with a group that was responsible for the computer software and hardware development for a CTP manufacturer. One topic that came up was a request from a press manufacturer for some software that would compensate for distortions of the print on a sheetfed press. The distortion that they wanted to address was in the shape of a trapezoid, where the head and tail had different widths. I am assuming that this kind of problem was due to differences in forces on the paper due to different coverage as the paper was released from the blanket, and therefore possibly stretching the paper unevenly. You suggest such a thing in your 1. point.
So there could be some potential for software to compensate such a distortion and at least one press manufacturer has thought of it. I don't know if the software was developed by the company I was assisting.
I also think there has been a press manufacturer, which has done some work to account for a distorted image in the press. If I remembered correctly, the ideas was to stretch the plate laterally at the tail. I might be wrong on this.
Manroland has a function where it adjusts the rate of rotation of its plate cylinder on each revolution to try to address fit problems in the machine direction. This might mean a higher or slower speed of that cylinder during the print part of the cycle and then a return to normal relative position of that cylinder in the gap part of the cycle. I don't know it they still do this.
My original point was that if some distortion was consistent, then one could adjust in prepress. Of course, as Alois has stated, it should be common knowledge by press operators on how to adjust the fit in the machine direction with changes in packing. I am not sure what the press operator could do with lateral distortion and its mis-registration.