I turned down the water effects and civilian traffic in Black Shark, and reduced the cockpit display resolution to 512. It runs fine now.
Making the same changes to A-10C also improved the performance enormously, though it was already acceptable.
I can confirm that A-10C performs better with Crossfire disabled. Haven't done a careful comparison of Black Shark either way.
I also overclocked my Core i7 to 4.5 GHz, which also was a dramatic improvement. Am debating whether to keep it there or back it off a little.