So if he releases F9/11 in June that would take it back to 9/01. Most of the press I've found shows that he doesn't mention the project until he's promoting Columbine in 02.
He probably started to "research" shortly after 9/11 based on all the conspiracy theories surrounding and while he was polishing up Columbine for release in 02. That would leave him with the rest of 02 and 03 to collect footage from various sources and eventually (based on found images) come up with his "special" part of the doc. Namely the "man on the street" hectoring he's known for.
So if I had to nail it down I'd say his personal "stuff" (interviews, guerilla camera crews in Iraq, etc.) were probably shot in the summer of 03 through the end of the year.