What you are telling sounds quiet plausible. I am in fact using a shielded USB cable but it doesn't have ferrites. The spindle I'm using is just a random 500w air cooled thing from China with included PSU. Do you think it will help to use shielded wires to the spindle? I don't have a USB cable with ferrites on hand but I should be able to find some shielded wires.
The only weird thing about this is that it doesn't happen when the spindle is on but only milling air.