Thanks for all the opinions and suggestions. Lots of ideas. Really, all I was asking was whether you liked the leaves better with or without the background piece, but your suggestions were interesting and varied. I tried to picture each one in my mind and consider the virtues of each.
Maybe you'll be interested in what I decided to do and why.
I took it apart, which fortunately was not very difficult to do with the help of a nice sharp and pointy seam ripper. You can see one of my lazy secrets revealed. I did not quilt the center stripe all the way. I left the area that was hidden by the leaves unquilted. I did decide that there were three elements here that were not sufficiently related to make them work together. Furthermore, I believe, as the critiquer and many of you believe, that the leaves need to stand on their own. That square is pretty strong and even as I was making it that was the part I was really loving and knew that I was doing it a disservice to force it into compliance with a show requirement. It will be properly finished and perhaps framed. The other pieces will go into my boneyard and may be brought out for future projects and I will move on to rethink the green line show and what I will do for that. (I am actually already working on an idea that might incorporate the white background piece).
Now, a little philosophising—take it or leave it. I was interested in the ideas some of you offered. Several suggested adding things to the piece to "fix" it. That always seems to be the first impulse and I have found, almost always wrong. In this piece there was too much going on already and adding more would probably have made it worse. This was a piece that wanted to be simple and calm, not complex and active.
For the same reasons, I rejected a couple suggestions that I needed simply to break out of the symmetry of the composition. I agree that asymmetry is often more interesting, but symmetry has its place, especially in work that is intended to be quiet, contemplative and focused. As disparate as the elements were, I felt that a formally balanced composition that focused all movement toward the calm center was my best strategy for making everything work together. It wasn't enough.
I actually liked the idea of dyeing the background a darker color, but not as much as I finally liked removing it altogether. It may get dyed, or painted, for its next incarnation.
I think the lesson, that was reinforced for me, was that usually, if you are willing to listen, the work will tell you what it needs. But it is awfully hard, sometimes, to back down from a preconceived vision, even when it's flawed.