Hi Matt,
I’m afraid this is the major problem with photographing birds at mid-day, especially if they are damp as well in the summer period. Bird’s plumages are reflective.
The sun is at it highest so the contrast goes through the roof, the haze also makes the bird look out–of-focus. Ideally, early or later in the day is best when you can achieve the ‘modeling’ light from the sun on your subject.
You can try to amend in post production the black in these images, but generally people over-compensate making the image looked ‘zapped’ by light.
I read your other post on calibrating monitors too, I wouldn’t worry that much, unless you have changed your procedures dramatically.
Colour correction has never changed whatever people think of in this 'NEW' digital age. Professionally it has always been done in an ambient light, so I would try and reproduce those conditions at home.
I correct at night with the hall landing light just giving me a low even ambient setting within the studio.
Calibrating is only a tiny part of colour correction. Generally people over-cook their images, an image should take less than 20 seconds to colour correct. That’ll give you a general file that you can then amend for use on the web or other reproduction at a later date.