Well unless you get a 500 or 600 (north of 10K as I am sure you are aware) , there is nothing you can do about the reach. I struggle with that all the time. One thing with my 7D though, and I don't know what you are using for metering, but with BIF I always switch to spot, as all that sky tends to make the meter want to underexpose the bird. Some people also use manual with auto ISO enabled, for example, f6.3 shutter 1/1000 and auto iso. I have done that with my 1D and been pretty successful , but I haven't tried it with my 7D.
Also, if you get the Nik plugins that are on sale, Nik Dfine does a GREAT job taking care of 7D noise.
At least you have Eagle to see! They don't get out this way very much, although they seem to be making a slow comeback.