Ok I've figured it out. I had started my flight using the mouse to manipulate the yoke for takeoff for speed (my joystick was plugged in just out of reach), and of course when you let go of it, it stays where it is. When the A/P was engaged it was fighting the yoke position.
I wiggled my joystick, which unstuck it, and my passengers have stopped barfing.
Cleanup on aisle 2 please.