A modeler is making a faithful recreation of the upper four decks in CryEngine[1], which is quite an undertaking because of the multiple, contradictory, and often physically impossible schematics used during TNG's production. CryEngine has some support for in-world user interfaces with mouse interaction (although Doom 3 still did it best), and with Awesomium you could hook it up to a more familiar CSS/HTML stack. Significant modification would probably be required to scale anything to the number of interactive displays on the ship, though. So get cracking on a robust LCARS spec, get the modeler onboard, get sponsorship from Oculus for a virtual Enterprise launch title, and make CBS a pitch they can't turn down.
[1] http://www.trekbbs.com/showthread.php?t=217183