As part of our basement renovation, we need to fur the walls of the small (currently 28"x40") water shut-off closet. The closet nook is being closed in with a door. We have already insulated the exterior facing walls with 2 inches of XPS and don't want to drill through the insulation and into the cinder block wall to use concrete screws. Our thought was to build a furred framing for each side using 1x2s and 1x3s (using PT where it touched the slab) and then attach the pieces to themselves, the ceiling joists, and the enclosing wall framing.
We are hoping to get some 1) validation that this would support the drywall and 2) suggestions securing the "bottom plate" (I was thinking PL Premium)?