I recall searching for that higher quality commercial / video. There were at least a dozen posts with the poor quality version and only that one descent quality version. Good idea to post it here for every to see!
Assuming the Dark Moss Green car is #0003 it was built 10/19/66.
There were 10 Bronze GT350 show cars all built within about a week of each other 10/31 - 11/8. The earliest were the 4 built 10/31/66 (#0059, 0060, 0075, 0078). All 10 Bronze show cars are noted as completed and shipped on the same day. If we knew when the commercial was filmed (or maybe when it aired on TV) that might help to narrow it down slightly. Still, without SA documentation, this question will be a tall order to definitely answer.
Of the 22 GT350's built, we can only rule out #0095 with the vertical grille.