I need to install a ceiling under some 9/12 roof rafters but i want to space the drywall out by 2″ to leave more room for insulation and reduce thermal bridging.  The plan is to put up 1×3 strapping with 15.25″ O.C. perpendicular to the rafters but space them off from the rafters by 1-1/4″.  I’m using mineral wool so will cut grooves for the strapping.  Quick mock-up in attached photo.

Is this a bad idea and how to best fasten the strapping and spacers to the rafters?  Don’t want to use too many fasteners and split the spacers so was thinking predrill and screw through strapping+spacer to rafter with 2 GRK #9 3-1/8″ screws: 1″ into the rafter should be enough to hold strapping and the spacer is just a spacer.

Is that enough?  If I start adding shims between strapping and spacer blocks and they get around 1/4″ thick, do I need to go up to 3-1/2″ screws?  Loctite PL the spacers to the rafters?