I think you might be out of luck there with the extensive use of hand tightening chucks on modern drills and the conversion of many of the bits formally used with a brace to fit three jaw chucks I cannot see anyone bothering to make a replacement chuck to fit drill bits that are now getting harder to find. I must admit I find augers used in power drills very easy to overdrill the depth owing to the screw guide feeding the drill in rather than the pressure applied by the user. If you have a number of brace bits that you want to use then cutting off the taper end off them might be your only solution.

Richard