UPDATE: I've found the issue that was making it difficult to take off and maintain flight in the buzzard. Holding the fast forward/turbo/afterburner button (default E, left shift) tilts the nose down. In first person you can see the pilot tilting the stick forward while holding the button.
The afterburner sound seems to kick in automatically if you keep holding thrust up, and the fast forward/turbo key has no effect on speed, only tilts the nose down.