Got 'em!!!!
My brother gave me a great idea. I slowly plugged all holes and crevices with plastic zip locks, and basically made it impossible for the tang to hide in its favorite spots. Once I had it trapped where I could see it, I drained the tank completely. I had to move two rocks with minor coral casualties, but I got it.
Total time from starting to plug holes to catching the tang, and filling the tank back up was about 1 hour. Corals are all OK.
I had to frag a few corals, and still need to re-arrange the rocks back, but overall very little collateral damage.
Pics to follow soon.