I'd definitely agree about troubleshooting each line. Just mute everything on the board and start activating channels on one at a time until the AM signal bleed turns up. If you isolate the channel(s) with interference, try swapping out the cables for shorter and/or shielded cables. Also try rerouting them away from other conductors, power lines, etc. If the AM is still there with everything muted, I'd check the line signals between the mixer and amp(s). Again, try using shorter shielded cables and rerouting them.
For what it's worth, my home setup gets AM signal bleed from a long mic cable. I've reduced it significantly with one of the A15RF XLR RF attenuators made by Shure. The real solution to my problem will be a shorter cable. My wife's mic (same model) doesn't have that problem. She's got a 15' cheapie cable. Mine is a super expensive long Monster Cable that will go in the garbage after I get a shorter, cheaper one. The attenuator has been helpful.