Though all answers here are correct, I believe the method I just thought about is accurate too. As mentioned in your question, this is some kind of a calculating trick.
- Select one of the two edges at the end of the bevel and put the cursor to the selection
CTRL+S Cursor to selected
- Select the opposite edge and seperate it from the cube with
Now switch to object mode and select the separated edge
Set the origin of the seperated edge to the 3D cursor (can only be done in object mode)
SHIFT+CTRL+ALT+C Origin to 3D Cursor
Still in object mode, apply a mirror modifier, in this case, mirrored on the Y-axis. Apply the modifier and go into edit mode.
Put the cursor right between the two edges by selecting them and pressing
SHIFT+S cursor to selected
Hey! The cursor is right there where you need it, that's the little
- Now you can go back into object mode and delete the object with the separated and mirrored edges. Select the Cube and go into edit mode, now select one of the two edges at the end of the bevel and put them to the cursor with an offset like so (You have to do this with both of the edges at the end of the bevel individually):
SHIFT+S Selection to Cursor (Offset)
- Now you have to delete the edges that are left between the bevel and fill the faces that are deleted through deleting the edges. Don't forget to remove doubles and you're done, the bevel is gone :)