If you can, you may want to look at the AA side. They're a bit more relaxed on the UM policy.
Our 12 year old flew on his own from MIA-DCA this summer. AA gave his dad a gate pass to take him to the gate in MIA. We probably would have gotten one at DCA, but we got there late. He ended up calling us and meeting us at the entrance to the concourse. It went pretty smoothly.