It occurs to me that you could make it even easier with the Dremel in a rigid mounting at say 45 degrees from vertical. It would need a height adjuster so you can set the burr at e.g. 1.4mm for 1.6mm FR4, and a repeatable lift/drop mechanism.
Then you could slide the FR4 under the burr, holding it on four corners to get more control. If would be easy to get straight lines this way.
For bonus points, operate the lift/drop from a foot pedal.