405 brass has too thick a rim to close the bolt with a round in the chamber. You need to find 38-72 brass. The rims were made thicker on the 405 so the action wouldn't close in the 40-72 as the 405 loads are more potent and could blow up the 40-72. The 40-72 and 38-72 were black powder chamberings before the 405 was developed.
I got a bunch of Jamison brass from Graf...
https://www.grafs.com/retail/catalog/category/categoryId/851Mike Venturino and I have just completed an article on the 40-72 and the 405 Winchester testing both cartridges and cast bullets in original 1895 Winchesters.
We are using 5744 powder and 408 gas check bullets. I can't say what you will want to use for the 38-72 without a bore measurement and choosing a cast bullet accordingly. Ours is a mould Mike ordered special for this project with a 320 grain bullet. I would expect yours to be a bit lighter, but you should be able to closely duplicate the same loads.
The article will be out shortly, I don't know which magazine he is sending it to, Rifle or Handloader...