I probably went overboard in saying that the gun accuracy isn't that important. Your Les Baer is a good example. But a 1911 style gun has a LOT more variables, like the busying tolerance and fit, etc., and yeah, the way government 1911's rattle when you hold them, compared to a quality assembled version (even my Colt Gold Cup National Match, for example), it makes a big difference.
But I stand by my statement that simply replacing the barrel of a SD-style handgun will not make a difference that the vast majority of shooters will see. I'd go to a Storm to get extra features, like a longer, ported barrel, but I would not expect a visible difference in accuracy from the OP's handgun.