Great news! It seems that my speculations about there not being a continuation of Tsubasa Chronicle were wrong. According to this site, a Tsubasa Chronicle OVA has been announced! The animation studio to handle it is still unknown at this point.
It’ll be interesting to see how this develops in the future. Obviously, an OVA won’t be enough to finish the story, as from the things I heard, the manga goes on for much longer. Still, this does show that CLAMP doesn’t give up after its debacle with Bee-Train. Perhaps we can expect more OVAs in the future, or perhaps even a third season.