This is theoretically possible, but introduces a lot of complexity. It also will have an impact on user experience, as the amount of drag would depend on the exact material being cut. Meaning, you might need to recalibrate any time you move to a different material, or possibly even thickness.
I think there are improvements yet to be had in the static model. The easy solution I see to addressing this would first be to minimize friction between the sled and the work surface. That won’t fix everything, particularly acceleration-induced dynamics as you mention, but it’s a start at least.