Unfortunately, it appears that the orbits of the Uranian moons may be off by 180 degrees.
Dated photographs of Uranus and its moons really seem to be scarce on the public parts of the Web.
Hubble took a picture of Uranus on August 14, 1994, revealing its rings and the positions of quite a few of its moons. See http://observe.arc.nasa.gov/nasa/gallery/image_gallery/solar_system/solar_uranus2.html and also http://hubblesite.org/newscenter/archive/1994/50/image/a. The picture shows Miranda at about the 4 o'clock position and Ariel at 10 o'clock.
(The only other picture I've found doesn't include Miranda, Ariel or Oberon, the three moons that Celestia tries to have accurate orbits for. It's at http://hubblesite.org/newscenter/archive/1997/36/image/a.)
Setting that date in Celestia, below is the best correspondance that I can get using a telescopic view of Uranus from the near vicinity of the Earth. The orbital periods of both Miranda and Ariel are significantly more than a day. This is the only view I could manage that shows them on opposite sides of the planet on the 14th. Ariel is at the 4 o'clock position and Miranda at 10 o'clock. Rotating the image 180 degrees would put the moons in the right positions, but then the illuminated pole of Uranus would be pointing toward the right instead of toward the left to agree with Hubble's view.
(this links to a higher resolution image)
