Definitely stick with the 7D unless you have a big, big budget to work with.... It's not just the lens multiplier factor. The 7D "puts more pixels on target" than either of the 22MP full frame cameras. The 7D has more than twice the pixel sites per square mm (around 54,000 compared to around 25,000). So for most anything that calls for long telephotos, the 7D will give you superior results unless you also change lenses.
You could achieve better IQ with the 6D or 5D Mark III, but in order to do so you'd also have to trade in your 400/5.6 for a 600/4 IS or 800/5.6 IS. That's a rather expensive upgrade. Especially since you'll need a top quality tripod to put the camera and lens atop, too... Plus a backpack to move the lens around.
And, I agree, the AF system of the 6D would be a downgrade, too, compared to the 7D. The 5DIII would be more equal to the AF performance of the 7D.
You would also be going from 8 fps that the 7D offers, to 4.5 fps with 6D or 6 fps with the 5DIII.
Be patient... I bet we see a 7D Mark II sometime next year. I expect that will be a great birders' camera.