I've seen welds done with MIG on guns. They all uniformly look like crap. If you want to weld on a gun, use TIG.
The comments about hardening the 4140 are spot-on. The only way to get the steel to not be hard is to post-heat it to let it cool slowly. Even then, you're going to get the hardness wrong - it will likely be too soft then.
Then there's the issue of the extractor cut. You need to remember that the 1903 has that Mauser-style claw extractor. Well, that requires a cut into the barrel to allow for that - except in your case, you'd be cutting into your bushing and the barrel.