.357 Magnum brass is longer than .38 Special brass so the former cannot be loaded into the cylinder of the weaker gun. You can readily load .38 Special brass to .357 pressures and shoot them in a .357 revolver with no particular problem.
That said, I would examine a charged case, and see how far you can seat the bullet before seating that-there bullet. As with any experimentation, start low and work up.
I'm happy for somebody to correct me if I'm wrong, but I don't think there is any more strength around the case-head of a .357 Maggie than of a .38 Special. You can always cut one of each longways, and mike them.
Whatever you work up, make sure you mark the loads somehow, so they don't wind up in a Model 36 or equivalent...