I have a Shumate Dollar that's similar to that. I consistently get great shaves from American steel.
American vintage razors totally rock. If yours is all cockeyed thats okay. Hone it until you got a bevel that meets in a proper edge. Dont worry if the bevel surface is not of consistent width etc, as long as you DO have a bevel, end to end. I would be extremely surprised if your Shumate is too far gone to hone and shave. Just keep at it. Use the burr method if there is any doubt. Get that bevel set and no question about it, and only then do you start your progression.