When I told Will what we saw this morning, he asked if I meant Sesame Street. No, not quite that big of a bird, but the same color: we saw golden orioles! Click on the picture for one link and here to listen to their song. They were beautiful, and the recording is definitely what we heard. Although, they screech like jays, too, as we heard and the article says. Jaan was busy in the mulberry tree, but Raia and Asya and I followed our orioles around the park for a while. There were at least two of them--a pair--but I think there were more, too. They stayed up in the tops of the trees, so even with their bright coloring, we only got glimpses.
If you go back to my mystery tree, you'll see that the mystery is solved. It's a Catalpa. Thank you so much, JennyBeth, whoever you are.