I was in New Orleans earlier this year as well and WBBM was booming in just fine. No sign of the Jackson, MS 780. In addition, 720 WGN came in fairly strong down in the Big Easy.
Speaking of picking up 780 WBBM on the West Coast, here in Phoenix, AZ, every now and then you can get lucky and pick-up WBBM. Most of the time, you have to null out KKOH from Reno, which is pretty easy considering how far away to the northwest it is from Phoenix. KAZM from Sedona, for whatever reason, is almost never picked up down here in Phoenix at night. KAZM must have a favorable antenna pattern away from the city. Even with these favorable conditions, it's still hard to pick-up WBBM. The main culprit being adjacent channel interference from 770 KKOB, which, along with WBBM, is directly northeast from here. But, if KKOH is weak enough and KKOB is not booming in like it usually does, you got a good shot at picking up WBBM. Sometimes I've been really surprised to hear it coming in fairly strong on a normal car radio. Usually the best time to pick up WBBM in Phoenix is in the wintertime.
Regarding 720 WGN, you can also pick that up here in Phoenix if you're lucky. Reception of WGN really depends on how strong 720 KDWN is coming in from Las Vegas. Lucky for us, most of those Nevada stations with signals on the Chicago clear channel frequencies (KDWN and KKOB), point most of their power to the west and away from Phoenix. Being southeast from KKOH, KDWN and KDXU give us a fighting chance to pick-up Chicago clear-channel stations. On the other hand, if you're in California trying to pick-up Chicago stations, you're pretty much out of luck. Every time I go to L.A., KDWN is blasting in on 720 AM, KKOB comes in surprisingly well from Reno and KDXU owns 890 from St. George, Utah. In my experience, the strongest station from the east that you can pick-up in L.A. is 850 KOA from Denver.