Thank you!

Best easiest way. You're Macgyver dude

Would it be easier to turn the pulley if the car is put in neutral gear?

The big wheel that this belt sits on is called what? as its not running true(with a wobble), so guessing I just need to replace this big pulley?

4pk810 is the factory belt of those engines. However, if you don't want to force the plastic pump pulley, and break it while installing that you may choose 4pk830 (810) elast. It is more plausible for the M47 engine. So, 4pk850 may cause squeaking, and may feel a harder steeringwheel. And finally, the best way to stop chirping sound when start and stop the engine is replacing the pulley with aluminum one if you may find, and using 4pk810 itself. The much tighter belt the less chirping. Even it will be completely gone. 🫠