Hard to say when not have the engine to look at.
But I think you problem are in the LU.
The pinion gear have to have right play/back lash.
Too tight the pinion gear will press at the forward and reverse gear.
But as it idles in neutral at 800 RPM and the press are at the F and R gear even in neutral, I would guess you have a too tight end play in the prop shaft.
The nut holding the bearing cage assembly for the prop shaft should be tighten so it will bottom the cage.
I interprets it as you have to loosen it a bit to be able to turn the prop shaft.
But I think you problem are in the LU.
The pinion gear have to have right play/back lash.
Too tight the pinion gear will press at the forward and reverse gear.
But as it idles in neutral at 800 RPM and the press are at the F and R gear even in neutral, I would guess you have a too tight end play in the prop shaft.
The nut holding the bearing cage assembly for the prop shaft should be tighten so it will bottom the cage.
I interprets it as you have to loosen it a bit to be able to turn the prop shaft.