Thanks for all the replies. I'm sort of leaning toward ETpilot's solution of starting in the garage and switching to the outbuilding later. I won't be getting a separate meter, so I'll end up burying line from the house to the building.

ETpilot, one thing to consider with the wheeled A/C units (or in my case, a wheeled heat pump): they exhaust air to the outside, but there's no incoming air. That air has to be replaced. I tried cooling my garage with one, but the exhaust air had to be replaced somehow .. in my case, it was coming in from the attic stairs gaps and under the garage door. So my 100 degree air was replaced with 100+ degree air from both outside and from the attic. I ran the thing but only got 10 degree cooling in the area around the unit. I ended up having to put a window A/C unit in the garage. Luckily it's hidden by shrubs so neighbors don't know about it. But there's no security when you have a window A/C - but in the Texas summer, security is secondary to A/C!