Earlier quoted context omitted.
If the problem turns out to be that AT&T and Cogent's peering links are overloaded, and the links between AT&T and Hurricane Electric don't have similar problems, then your border routers should be setting localpref to something low for any route with AT&T's ASN learned on the Cogent BGP session, which should send your outbound traffic to AT&T via Hurricane Electric except when your he.net link is down. The opposite…
I tried switching my outbound traffic to the customers in question over to he.net (with a static route, which I know is the dumb way to do it.) with no improvement. Hm. I need to learn more about bgp, specifically tags and communities, can you recommend me a book?
You may want to define communities to let your customers selectively decide to suppress announcements to each of your upstreams, and you may want to pass through the communties recognized by your upstreams in their official documentation if your customers send those communities to you, if you want to let your customers control their advertisements in that fashion. (The only reason I can think of you wouldn't want to let your customers do this is if it would let them move traffic from a link that's cheap for you to a link that's expensive for you.)