Let me see if I got this right.

You fasten the portions of 2x4 to the joists, lengthwise, near the bottom edge, but up a bit, so that the bottom of the rail that you fasten the drywall to is only 1/2 below the existing joists.

These 2x4's would need to hold a lot of weight. I think I'd use liquid nails and a couple of bolts to hold them in place.