You can also change the AE Lock* button on the camera (via custom controls) to an AF-Stop (AF-Off) button regardless of what type of lens is attached. I prefer Back-button AF-On for Auto focusing and tracking in AI Servo (in conjunction with removing focusing from the shutter button), and then just remove my finger from AF-On to stop tracking and lock focus.
Kevin, it sounds like some custom configuration settings are way off, or you've got yourself a serious problem with 3 cameras. However, it would be highly unlikely that all 3 cameras would be bad, so it must be a custom setting somewhere, but AF-stop should not behave like that. You can reset your camera as was suggested above or first try resetting Custom Controls. When you're in Custom Controls if you hit the Trash Can you can set those settings to Default-set.
As you've mentioned above, the AF Mode (AI Servo or One Shot) should not have anything to do with Drive Mode (single shooting or high speed continuous shooting). Even if you limit continuous shot count, it shouldn't be different for One shot or AI servo. The only way that I know how to shoot in different Drive modes and AF Modes, would be with Custom Shooting Mode (C1-C3) and the AF-stop button or custom controls shouldn't change your setting to Custom Shooting Mode. The only way that I think it could be done would be by setting the "C1" (Custom Shooting Mode) to AI Servo and Low speed continuous shooting and have Manual mode set to One Shot and High speed shooting and then set custom controls to M-fn to to 'C" and when you hit M-fn it would switch your AF mode and Drive Mode from 'M" (one shot and high speed) to "C" AI Servo and Low speed). But you would be well aware if you hit the M-fn button.
What shooting mode are you using, AV, TV, M, C?
Who set up your cameras? Did they use the same configuration with all 3 cameras with a CF card?