One of the most accurate 1911s out there is going to be a Les Baer with the 1.5" (at 50 yards) guarantee, but I don't think you're going to fit that into a 1500 dollar budget, even used.
I have a Custom Target II with a little more than 5000 rounds through it. After it had two failures to return to battery while it was still breaking in between 200 and 300 rounds, it has not failed. The "extractor problem" was with their earlier external extractor models, which they no longer make. A friend has one, and it has yet to have an issue in 3000 rounds. The Kimber target sights are excellent, and the gun is fairly accurate. Not accurate enough for my tastes, so I ordered a 1.5" Baer.
I think the most important question in picking this gun is how accurate are you? Do you shoot handguns a lot? Are you into bullseye, or some other accuracy-centric competition that you practice regularly for? I'm not making assumptions on your skill, just pointing out that I've heard a lot of new handgun owners or people that don't shoot handguns much looking for "the most accurate pistol" when the truth is the way they shoot they'd never see a difference between and RIA and a Baer. Knowing how well you shoot can go a long way to avoiding throwing away money for extra accuracy that you'll never be able to take advantage of.