I called Motech last year and got an estimate for a 6.3 LS3 conversion on a 2011 JKUR. They told me $19,300. That included all parts, labor, and sales tax; all you have to do is drop it off, and then pick it up again 10 days later.
Motech is in Las Vegas and they specialize in LS3 swaps.
2014 Wrangler Sport: Teraflex/Synergy 3" suspension lift, Fox 2.0 reservoir shocks, Tom Wood 1350 driveshafts, Dynatrac ProRock 60s w/ 4.56 gears and Eaton electric lockers, Warn front locking hubs, Currie Anti-rock front swaybar, Fox ATS, 37" Toyo MTs on 17x8.5 Vision Warlords, Poison Spyder bumpers and rocker guards, Warn M8000s winch, Teraflex tailgate hinge & spare tire carrier, Mopar head liner