Luckily the can of Army Painter matt black undercoat was more than up to the task.
They were indeed based on the Black Swans section from BtCV.
Here's a close-up of the Bloodhawk, which is piloted by Erica "The Streak" Boch:
And the Firebrand of Susan "Billboard" Moore:
I was pleased with how this one turned out.
I tried to keep the paint job as close to the CS lore as possible, but as it would be a nightmare to keep track of 36 identical planes in a game (and I'm not keen on base ID markings) I tried to make each one as unique as possible but still look part of the squadron. Each flight has its own coloured propeller spinner, for example: First Squadron are black, Second are white, and Third Squadron have red.