From a practical point of view have a think about the radius of turn at say 100Kt and 45 deg AOB. It is not very big. One could say that any aircraft that collides with you while doing a steep turn was probably going to collide with you anyway, or at least get so close as to be an Airprox. The large rapid movement of the aircraft entering the steep turn may just be the visual clue that actually highlights the aircraft and enables the other aircraft to see and avoid.
Doing a long detailed HASEll check means spending more time looking inside or close to the aircraft while flying in a straight line which actually increases the collision risk.
I would go for a good lookout and leave it at that.
Why would one ever do a 360 deg avoidance turn? The answer is simple;
You are converging with an aircraft on your right at the same level and do not spot the aircraft that you are required to give way to until it is too late to turn behind. The other pilot maintains heading and speed. You complete a steep left turn through 360deg or slightly less and pass behind the other aircraft. Thus while not an ideal situation you manage to comply with the rules of the air for converging traffic.
Regards,
DFC