I have done the flower garden trip out of Texas and they usually do some rigs. I think rig diving is great, but wouldn't want ot burn the whoel trip from chicago doing just that. so for rigs and some typical carribean diving, this trip is good. It's a liveaboard (MV Fling or MV Spree). good crew and good value, only problem is that the weather can cancle you trip.
During the winter months the same crew does some short live aboard trips with the same boats to the Dry tortugas, might want to check that out. here is their site http://www.spreeexpeditions.com/
Other rig diving alternatives are out of LA and MS areas
Also, I find the diving out of either Panama City or Ft lauderdale (or lauderdale by the sea) to be excellent and great value0