I spoke with Canon Canada and they've instructed me to send the camera to the service centre in Mississauga.
Right out of left field.
Canon has announced a new AF fix for the EOS-1D Mark III and EOS-1Ds Mark III. This is in addition to the sub mirror fix issued earlier by Canon, and requires returning the camera to Canon for service. New firmware for the 1D Mark III and 1Ds Mark III has also been released to fix issues with live view, USB communication, and to update camera error codes. This brings the versions up to 1.2.5 and 1.1.4 respectively, and is available for download now.
How to get the best out of your 1D Mark III
Download the firmware
1Ds Mark III 1.1.4: http://web.canon.jp/imaging/eosd/eos1dsm3/firmware-e.html
1D Mark III 1.2.5: http://web.canon.jp/imaging/eos1dm3/firmware.html