I too have had his problem. My vehicle is a 2002 Avalanche. Elecronically, its the same as the Suburban and Tahoe. I tried some split beads, but wasn't happy with the results. My mobile setup is a 706 MKIIG and either an ATAS-100 or Hamstick. So, I intercepted the 12 V supply to the amplifier, installed a toggle switch just under the dash and to the left of the console I could reach easily while driving, and just turn off the audio amplifier when I want to use the rig. That worked for me.
73 de John, WA5WFE