Well, this has been quite a treasure hunt!
After a lot of time staring at code and Atari documents and looking at many frames and scanlines, I think I understand what went wrong here.
All of this comes down to a color clock delay in drawing double sized players. Bizhawk misses this delay and thus double sized objects, such as Pterry and the countdown numbers in Flapping, are drawn one pixel too far to the left compared to real hardware. Those interested can download the neat test ROM from this thread and compare BizHawk and Stella, pretty neat demonstration!
http://atariage.com/forums/topic/239890-respx-nusizx-and-player-positioning/
Anyway, this is not simply a graphical glitch, for the TIA also does hardware level collision detection, and in a literal case of threading the needle, this is where things go wrong.
After I understood the difference between inputs in Stella and Bizhawk, I was able to compare frames and see where things went wrong, and it all comes down to that one pixel shift. Illustrated below is the frames right where the game diverges between Stella and BizHawk:
Stella:
BizHawk:
So in Stella we see that, in an amazing coincidence, the ball moves directly into the birds eye! So the TIA does not count this as a video collision, and the ball carries on for one more frame. But, this isn't the case in BizHawk, that one pixel shift means that the ball and the player collide 1 frame earlier, and everything diverges from there.
In the end, the Stella game goes on to lose, while the BizHawk one goes on to win, all because of 1 pixel of shift due to an obscure hardware level delay.
there is still more to research and AtariHawk is doing several other things differently from Stella, but for this game this is the deciding factor.