Thankfully, this is fixed by a small change in procedure!
When presented with the following screen, do not over tighten the nuts. They only need to be lightly finger tight. Then continue on like normal.
If the three nuts are tightened too much, they can 'clamp' the bed in place. This then means that when one nut is loosened, the bed is held still, rather than allowing it to move upwards towards the sensor.