Piltdown and Dani, by choosing to land without a clearance you are bypassing one of the fundamental safeguards of our operation. Because the radio is busy is no excuse.
As for the GA manoeuvre, would it be the same as at flight-school: zigzag/sidestep at below 500ft to establish some lateral separation from the departing aircraft and so you can keep an eye on him? Who's the PF? Go left or right? An interesting predicament and probably one not discussed often.