Just found this – Sound proofing a garage
Roof idea looks useful, although they are plugging their products. Remember mineral wool does little to stop sound transmission on it’s own. It’s main function (in a cavity) is to damp any resonances within the cavity as these can impair the sound insulation of the structure/system as a whole.
Are you able to position the garage doors so they face away from neighbour. This will reduce the impact of any leakage
EDIT:
Actually I have a slight issue with this
The 2 layers of plasterboard on resilient bars is all good, but the additional layer they’ve stuck in will do little (the “another layer of plasterboard”). It might even make things worse. The resilient bars should be straight onto the joists