Looking to upgrade from the factory barrel.

Very good replacement barrel. Charles the Gunsmith.  

Yes.

If the gun runs OK currently, why do you want another barrel?  The $300+ you'll spend on a barrel, bushing, and fitting is probably better spent on ammo and a class.

Most factory barrels do just fine in the accuracy department (they will shoot better than any of us can take advantage of).

I have a Baer with the 1.5" accuracy guarantee (10 rounds into 1.5" at 50 yds using Hydrashocks, Golden Saber, or WWB).  Best I can personally do is 4" at 50 yds, and that's prone, slow fire.  However, at less than 25 yds, I don't shoot this pistol much better than any of my other 1911s.

Barrel fit is more important than what barrel you have.  

Training/practice helps.

Ammo choice is also important.  A pistol that won't group well with ball will often do much better with quality ammo like hydrashock, golden saber, or match quality ammo.