IMO, I think you need to pump the brakes and rethink what you're after.
You want to bore some a 2+" deep hole into some sheet goods, far from the edge.
A router and properly sized template is what most of us would use.
You seem to be trying to attain extremely tight tolerances, can we ask why?
2 1/2" bit shown, Amazon, easy
IMG_6194 (600 x 400).jpg
If you're concerned about .25mm (.009") variance, you're using the wrong material. Insert a metal bushing to achieve those tolerances.
We're only trying to help but more info is needed.