On the subject of big white image quality, I am surprised on two counts. The 800mm f/5.6 holds its own compared to the 600mm f/4 II and the 600mm f/4 III. And the mark III's IQ is not really an upgrade, depending on how much CA annoys you. God it must have been years since I've looked at these super telephoto charts.
I have found the III overall somewhat less sharp in many areas depending on which extender you use, but with less red and magenta CA. But it has this weird blueish/low contrast hue with extenders. Especially compared to the II and the 800mm. It probably would not be as noticeable in the real world because pics are not usually black and white lines. But you are not really gaining IQ with the III lens as a whole and defiantly loosing some with extenders.