Personally, as long as there isn't some rule with your TA that prevents you from doing some things for yourself, I would try to make the ADR. The online system rolls at 6:00 am ET and the phone lines open up at 7:00 am ET.
Are you staying on-site? If you are, then you can make ADRs for the first ten days of your trip on the 180-day mark. So you have 10-days to work with to see if you can get a BOG ADR.
Now, it's worth noting that even if you can't get a BOG ADR at the 180+10 day mark, don't lose hope! People's plans change and cancellations do occur. When I'm going to WDW, even if I don't get the ADR I want at my 180+10 day mark, I tend to check daily to see if anything opens up and I've almost always managed to get it at some point (sometimes within a few weeks of leaving for WDW). So it might take some work (and patience), but there is always a chance that you'll get the ADR later.