The Pegasus in the Harrier has LP and HP spools rotating in the opposite direction (to minimise gyroscopic precession in the hover
Correct. Precession meant everything changed by 90 degrees once you got into the hover. For instance, if you wished to yaw the nose to the right you pushed forward on the control column. Pitch the nose up = roll right etc. It was quite easy once you got used to it but the transitions to and from the hover were considered quite tricky manoeuvres and the classic Harrier 'steep climb' from the hover, performed at air shows, the trickiest of them all.
To add a fly to the ointment, Coriolis meant reversing everything in the Southern Hemisphere (remember it was already contra-rotating, so there's no ability to swap the direction of rotation). Embarked on a ship, this involved a LOT of concentration having crossed 'The Line' and having to do it all over again on the way home wasn't too much fun either.