Truth be told, if the minimum height a kid could ride and still be safe were 40", the height restriction would be 44". They undoubtedly put a little buffer in there.
My daughter is in the same situation. She wants to go on Splash Mountain, but it will take a monumental growing effort to get her to pick up that inch by May. We did get my son on RnRC one year by stuffing napkins in his shoes. He wimped out when we got to the actual loading area, but still
I worked at a theme park in my younger days, and you need to be to-the-letter with the height restriction. If you let one 39 1/2" kid on a 40"-restricted ride, you need to let them all on, or you'll really have a problem. It's much easier to deny kids with the backing of park policy than on your own discretion. Also, if you do that, then you start having the 39" kids' parents complaining.