One of the good things about the LHT Complete is that it's pretty much good to go. There are only a couple of tiny tweaks that I can think of: better brake pads, a handlebar to your liking, tires that suit your use, a better saddle.
Maybe you can get the Complete from your LBS, and tell them you want to assemble it yourself.
Although one plus of buying the frame and parts separately is that you'll probably get the frame quicker - Completes tend to sell out, iirc.