One thing you might try is _not_ using spot metering.
I used spot metering and center weighted average + AE Lock and recompose almost exclusively on my XSi because evaluative metering was _terrible_. This is not true on my 7D though... and I bet the 5DIII is better.
Here is the bit from the 7D manual:
"To complement the iFCL metering sensor, the EOS 7D also features a newly designed metering algorithm. The EOS 7D always measures focus with all AF points regardless of the selected AF mode. During the exposure reading the EOS 7D looks to see which points, in addition to the selected point, have achieved or almost achieved focus. This information lets the camera know which part of the image is the subject. It then takes metering readings from the zones corresponding to the AF points that have achieved (or almost achieved) focus and combines them with readings from all the other zones. This allows for consistent shot-to-shot exposure, even in complex situations – where there are reflections from a model’s glasses for example. "
In practice, this is working really well for me. I haven't felt the need to go back to spot + AE Lock since I got the 7D.
BTW - On the 7D I've found that spot _AF_ seems to not work as well with the evaluative metering mode (it probably gives less info to the algorithm). So in cases where I'm really needing the metering to be good I just use one of the other AF modes (even Single-point works fine).