I'd say a nice LHT shop build should run around $1200-1400 with mostly new parts and maybe a few used ones (an old 110 BCD MTB crank, used front derailuer, old Nitto bars maybe?) It's easier if you have bike buddies with lots of old parts lying around....
I'd start with finding a set of high quality used brake levers and pair them with new bar-end shifters. This set up is cheap and unlikely to fail for miles of hard riding. Stay away from using STI brifters unless you have more $$$. I'd try to stay with 105 or Deore LX level parts-- they offer the best value for the money.
The bike shop should give you a deal on the frame-- close to wholesale, if they are building up the bike. Trust me, the shop will make plenty of money of labor and parts. It would be hard if you don't have a bunch of bike shops around. Here in the Northwest, there are so many shops that one of them would be more than happy to give a person with 1200 bucks a deal.