Photographing Birds in Flight

I have a 70D and 100-400 II lens.

I'm not totally pleased with how slowly it grabs focus with birds flying. But that's not the question.

Birds don't fly for us they fly for themselves.

When a bird is above the tree line the bird will normally be under exposed because of the bright background.

When the bird is below the tree line the bird will be over exposed due to the darker background.

I use either single or 9 point focus depending upon the situation. But that's irrelevant with this question.

If I use spot metering the chances of me having the bird right in the center is pretty low. If I'm really lucky I'll have one in the center.

If I use evaluative metering then the problem I'm describing is what I'll get.

Any quick change solutions?