Various reasons I don't suggest it. You can screw up and really badly scratch the frame from the saw/file. You might not have the patience/skills to get the HS bearings parallel to each other (the goal of facing), If the frame were a lugged one and having stamped (not cast) lugs you can open up a cavity in the crotch of the joint. If the headset cup skirts are long or you cut off too much the skirt might bottom out before the cup was seated. Because if you're the original owner any warranties will be voided. And because of the general philosophy in the repair business of not going to non reversible results if at all possible. I'm sure others could add their reasons.

Try the low stack height headset. Depending on the OEM VS the possible replacement HS you might gain as much as 7mm, on paper. If this isn't enough let us know. Andy