I knew I'd get some great replies! I posted the question, went off to spend an hour or so working on the quilt, and came back to all these helpful recommendations. I love this board!
I'm certainly going to persevere until the binding is done, because this is one of many ufos that have been around too long, and I'm determined that this is the year that I'm going to stop procrastinating about quilting and binding them, and get them done.