Hello
2.7mm end float is far far too much. It should be approaching zero mm and ‘free to rotate’, not clamping the lead screw.
I do not know enough about S7s to advise you what to do exactly, but someone else will. It would be useful to know if the machine is fitted with a quick change gearbox, and also provide photos of the bracket / lead screw arrangements at both ends of the lead screw, if that is possible.
Best regards.
Alan