I recall one of the first mid-air collisions relating to GPS tracking was in Canada. A Metro and another IFR twin, one on climb and the Metro on descent, nose to nose. I recall that the twin had rolled hard one way after what the investigators suggest was a late observation of the conflict. The report suggested that if he had pushed or pulled the collision may have been averted, but because he rolled the vertical profile of the twin was increased significantly causing its then upper wing to slice the wing of the Metro. Lesson there is don't roll to avoid in such circumstances. And yes a one mile offset is a good idea, especially in some airspace. I doubt if en-route radar could pick that up?
I found the ref, an interesting read and still valid some 25 yrs after the event...
https://www.bst-tsb.gc.ca/eng/rappor.../a95h0008.html