OK, so you can't access the space from above-fine.
Cut yr CLS to the length between joist and the strap on bit, skew screw CLS to existing (so the underside of the CLS is touching the upper surface of the plasterboard), put your board patch in, fix thing, done
Cut yr CLS to the length between joist and the strap on bit, skew screw CLS to existing (so the underside of the CLS is touching the upper surface of the plasterboard), put your board patch in, fix thing, done

