The only solution I can offer is unfortunately pricey, as it requires PS+, initiate the Auto Update for game updates, set it to the current timeframe and then turn the PS3 off, it will turn back on automatically in a black screen with text explaining Auto Update is in progress.
Wait a couple minutes and turn the controller on to exit the screen and proceed back to the XMB, you should notice the patch is background downloading in the Network section because GT6 was the last game you played. It will download uninterrupted as you browse the web or play light games that don't stop background downloads.
EDIT: NVM, you got it solved.