In 2012 Buie, Tholen and Grundy wrote a paper The Orbit of Charon Is Circular
Their models of tidal evolution predicted the Pluto/Charon would have a nearly circular orbit, an eccentricity very close to zero. There has also been speculation that obliquity is close to zero. Their models were somewhat supported by Hubble observations. But as we all know, Hubble images of Pluto and Charon are pretty low res. I am wondering if data from New Horizons has verified their predictions.
If so, this would make for a neat science fiction setting. With 0 eccentricity and 0 obliquity, the Pluto-Charon Lagrange 1 would hang motionless in the sky of Puto as well as Charon. Just as a Clarke tower would extend up and down from geostationary orbit, a Pluto-Charon elevator could extend Pluto-ward and Charon-ward from the Pluto-Charon L1. With 0 eccentricity and 0 obliquity, a beanstalk linking Pluto and Charon would not be flexed, stretched or bent by orbital motion.
The two dwarf planets could be linked. It would be a setting somewhat like Robert Forward's Rocheworld.