Have you thought about getting some hands-on professional theater stage management experience before deciding to transfer and starting fresh? If your college or area has any kind of theater, getting involved there might be a good way to start. Or maybe there’s a way to to an internship during intersession or the summer. Keep in mind too that there are plenty of people working in theater with degrees in another area. It doesn’t have to be all or nothing.
With a career in stage management, expect the same kind of lifestyle that you’d have as an actor. Whether it’s a solid markert or not depends on how you define solid. You need a high tolerance for change and uncertainty to be happy with this as a career. Even if you’re an amazing SM, there’s no guarantee you’ll have year-round work, or work that pays enough to live on, just like a talented actor might go a year without being cast. There are other threads on here with thoughts about making it to broadway, if that’s what you mean by large-scale. But remember that success and a sense of accomplish aren’t necessarily defined by the size of your productions. Stage Management has been my bread and butter for more than six years, but it’s not for everyone. There are some threads here about people’s plan B, or about transitioning out of SM’ing; you should check out those too as you think this over. Generally I'd only suggest a career in stage management to someone who really isn't happy doing anything else, because there are just way to many downsides if you don't love it.