I'd say get the LHT, though still try out the CC. Since you already have a road bike when you do want to go fast(er) the LHT would make a fine commuter.

I commute on the LHT myself. I originally bought it for the purpose of commuting and doing a tour I never got around to. It is definitely a comfortable ride. I guess I could change some things around if I wanted to go faster, I just enjoy the laid back feel of it.

Also, don't limit yourself when looking at bikes. Ride as many as you can and determine what factors would be important to you. When I looked at touring bikes I test rode the Cannondale T2, Trek 520, Jamis Aurora, and Surly Long Haul Trucker. For most factors I was looking at the LHT ranked pretty high though was only the top in one or two of the categories.