My guess: early September is too late for the GDMTR.
I read many GD blogs, both NS and NS rides, and based on these and my own GD rides I drew a chart to highlight the seasonal windows. Please regard the contours as soft. This is not rocket science because the climate conditions vary from year to year. It also depends on the pace you are able to go. The faster you go, the earlier you arrive at the high passes in southern Colorado, which I think are the most vulnerable to getting blocked by snow. I would guess that if you get to NM before mid-October you are OK and maybe need to make a few bypasses.
I certainly haven't read all blogs from late starters, but here you have two. One is from a guy who started on August 20 at the Canadian border and made it to the Mexican border early November. but met nasty snow and mud on some passes.
http://www.crazyguyonabike.com/doc/?o=1&doc_id=4227&v=DC#98352The other blog is from a guy who left Banff around mid-September and by mid-October decided to deviate from the GDMBR south of the Tetons because of the snow and cold.
http://www.whileoutriding.com/usa/idaho-and-wyoming/jackson-wy-to-flaming-gorge-utI also guess there are many bikers reading this who maybe do not have an overall knowledge of the GDMBR, but can provide more reliable information about the local bottlenecks in this chart.