No there is nothing special you can do to access ATT if they are down. If they are down, then they are down, and you can't access them if they are down because whatever hardware is out that services your area is going to be out no matter what you have.
The only thing you could do would be get an alternative service. Cell phone providers, for instance, have internet service, but you already have ATT as your cell phone provider so it would mean dropping them and getting a different provider.
If you have access to a cable company that also provides internet, that's an option.
Satellite internet is a possible option.
I understand your frustration when ATT goes down since you rely on service for your business. But unfortunately there is nothing you can do with respect to ATT when they are down all you can do is look into getting an alternative service. If alternative services are not available in your area, or if you are not interested in changing, then the only thing left I can think of is you would have to drive to a nearby city on those days ATT is down and do your work from one of their hotspots (provided of course their hotspots aren't ATT serviced that also is impacted by the same hardware failure causing your area to be out)