I added one more photo with a better background and more interesting perch. The difference in brightness between subject and background was still more than 3 stops, so it took a lot of tweaking, but I'm at least satisfied with the results. Both of these were taken at a recreation area on the Clarks Hill Reservoir on the GA/SC border.
I need to put a feeder behind my house and set up some natural(-looking?) perches in front of a nice background. Make the birdies come to me instead of the other way around