The auto iso trick works a bit better using spot metering with the spot linked to the AF spot ..... that meters for the bird and ignores the background. I've noticed with evaluative metering that often exposure compensation is needed to get the bird right because, as you said, the entire scene is being metered. With practice it isn't too difficult to dial the exposure up and down as needed .... with this technique I use Manual mode mostly. Once you acquire a good understanding of metering and exposure you can make it work in many ways.