I have a Springfield GI, but I like the polished barrel of the Mil Spec.
Where can I go to purchase this barrel?
You can send it to Springfield, and they will fit and install any barrel you like. Call their custom shop off the website.
While it's there, have 'em put some real sights on it, polish up the trigger action a bit, and check the springs... When she comes home... New Gun.
You would have to decide if you want a fitted barrel or one that will drop in with no fitting. http://www.midwayusa.com/ has several different makers barrels by several makers. I would advise that if you are doing that get a good bushing too.