The gin I was thinking about was shimmed on the 'sides', I don't recall if it was shimmed on the ends.  I do remember if the bale was over about 520# they would press it, hold it there and then after a couple of minutes (they were only ginning 4 bales/hour) would try again and  usually get enough so the ties would work.  They also had 'extensions' for the ties that were about 8-10" long they would use if absolutely necessary, if that didn't work they had to remove some cotton.  Now that was a sight, you'd never imagine how much volume a few  pounds of cotton takes up.  FYI the compress would charge extra for those larger bales but the local gin would pick up the charge for that.

Now the compress in Needville was actually a shop built contraption for a press.  It wasn't pretty but got the job done.  I don't recall the man's name that built it but they hired him to run it so he could tinker with it as needed.