Remove the furring, attach clip to the joist, and run the channel perpendicular to the joist, like in SPC Ceiling Solution 3 here: http://www.soundproofingcompany.com/soundproofing-solutions/soundproof-a-ceiling/
You can save an inch if you block between the joists in a recessed fashion, then clip the blocks, and run your channel parallel with joists. Channel face should be 1/4" lower than joist to avoid any drywall touching the joist. This is more work, and only saves an inch... might not even be noticeable in the end.
You can save an inch if you block between the joists in a recessed fashion, then clip the blocks, and run your channel parallel with joists. Channel face should be 1/4" lower than joist to avoid any drywall touching the joist. This is more work, and only saves an inch... might not even be noticeable in the end.