OP, not sure where your home airport is located, but I'd suggest looking at nearby airports. I've found good award tickets from Birmingham via Atlanta, when the Atlanta-destination flights were 3/4 times the price.

I've also found that JFK to, anywhere really, is significantly cheaper than elsewhere, even when factoring in a positioning flight. So you could do two tickets, one from AAA-JFK, then JFK-BBB.

Also, check out prices from competing hub cities, such as IAD, CLT, IAH. If you have a Delta Amex, and the cash tickets are cheap, you could do pay with miles. Not a great value, but sometimes that's better than the award price.

I've had success in finding cheap Delta One tickets by picking my destination and doing the five week search for one way flights there, and a second search for the return. Then plugging in those date for a round trip. I've seen the past two years Delta offer spring D1 sales for 99K miles rt. I got a rt ATL-DUB two years ago for 99K miles using the above method.

You could also try flying AAA-Europe/Asia on one ticket and then Europe/Asia-BBB if you want to get to South Africa or Australia. The issue here is the amount of time it would take, as you'd need a nice buffer between tickets. I'm also not sure it'd be any cheaper than USA-BBB, but you could try.

Good luck!