Dixie's Japanese repro has been out of production for several years. Might find a used one. At the end, they sold off kits.
A plain octagon barrel would work. Will this be a rifle or a smoothbore? Japanese originals were smooth.
True seamless steel tubing has been successfully used for a lot of smoothbore ml barrels. Catch is, a lot of "seamless" tubing is finished so that it looks as if it wasn't made with a welded seam. Smooth finished inside and out, but there is a robotically welded full length seam. There is actual drawn seamless tube available.
You mentioned 12L14. Leaded screw machine steel. Machines beautifully. A lot of ml barrels have been made from it. It has a tendency to be brittle.
1137 is outstanding for ml rifled and smooth barrels.
4140 has been used, but might be overkill. Popular for smokeless centerfire barrels.