You need a spindle ER11 collets as you say.


The play in the Z is either from the ballscrew nut, ends or from the rails and carriages. If the play is in the ball screw nut , you need a new one 0 clearance., pour graphite epoxy in the ball nut or print a 3d ballnut with a tight fit. If its from the ends its the bearings, change the bearings. Check that connection from ball screw to motor.

Machine like that is full of problems and the more you think the more you will want to smash it. But if you analyze the problems you can find the solution easy and dyi the solution from things laying around in garage. It does not have to be pretty