For $400 you could have your choice of many high-quality barrel blanks and have it installed. In my order of preference, given the price range: PacNor, Hart, Shilen, Douglas, ER Shaw. There are other barrel makers who make great barrels, some more expensive, some about the same, but these are the ones fit into your budget and that I have experience with or personally know someone who has one.
Some barrel makers offer accuracy guarantees, but typically only if they do the work, and onlyin certain actions with certain ammunition. But any of the barrels mentioned will be a very high quality barrel, capable of outstanding accuracy.
Something to consider, given the age of weapon you currently own: consider buying a newer rifle such as a Remington or a Ruger in the caliber you want. The newer rifle will be much more rigid and capable of better accuracy, while still retaining the eye appeal you seem to enjoy in your 96 Mauser.