You can make usable cases for your .38-44 Target by trimming .357 Maximum to cylinder length. They'll swell a bit, but at BP pressures, it should be no trouble. Case mouth should seat .005 -.010" shy of the end of the cylinder.
You may use a 148gr wadcutter seated full flush over a light charge of 231, or a 158gr LRN seated deep against 15-16 gr FFFg.
Let us know about your results

Larry