ER11 chuck to 775 motor -> DIY CNC machine, too much play

Hi, I'm trying to attach an ER11 chuck to a 775 motor to use as a spindle for my custom CNC machine. The machine is meant to make circuit boards so a 775 motor is good enough for that. Perhaps wood engravings could work too.

The issue is however, the chuck I'm trying to attach has way too much play when putting it on the shaft. The bottom of the ER11 chuck is not flat either so pushing it all the way down to the motor is not working.

The goal for this setup is to mill traces of 0.2mm wide. Perhaps 0.1mm if the V-bit allows for it so it should be on as straight as possible.

I have tried putting the chuck in the freezer overnight in an attempt to make the hole a bit tighter but that was not good enough.

Is there a good method to do this? I could just order a readily made 775 spindle from Ali but that seems a bit wasteful.