I wonder if you tried an HDR-type effect, where you deliberately underexposed a shot, overexposed it and then merged it with your normal exposure. That might help to capture a different color in the background, and also make the flowers stand out more... just a thought.
@donhoupt Don, I very much appreciate your response. I haven't done much in HDR. I have an HDR setting on my camera, which I used for a few shots. I probably should get the tri-pod out to use that in order to make a difference. Part of my issue is that when my eyes see the tree all it up from the sun, I don't see all the branches. If I get a large part of the tree in the photo, I see small flowers. If I get closer, the jumble of branches seems to make it "busy" for me. I may be running out of time. Fewer flowers on the tree today.
The tabebuia trees certainly make great photo ops. I did one a couple weeks ago and am tempted to take more. This is a lovely shot against the colorless sky. Different....I like it!