Moving the ship does break it. But activating modules does not. Targeting does. So the trick is basically to cycle AB on overheat for maximum effect, then at the end you just warp to the best spot.

You stay in the invul timer when you exist a abyssal site, don't do anything. If somebody is waiting on you you preoverheat the AB cycle it which doesn't break invul timer, then near the end you don't let it repeat and warp at the last like 10-15% of the cycle