I don’t have an complete answer for you, but am also curious about the same thing (for the same reasons). I think you would be able to go to your DM but you would have to be comfortable explaining that your manager is the issue. When you talked to the other store about transferring, what did you tell them the reason was? The managers in my district all know each other and are friendly so I wouldn’t know how to go about it.

When I’ve done that I’ve always made up a believable excuse along the lines of: “I want to transfer closer to my house”, “the hours at the other store for my schedule better” or “I’d prefer to work at a cafe/drive thru instead”. If you want to become a shift it’s possible to transfer so that you can promote if your store doesn’t have a lot of opportunities.