> The biggest difference I see between software developers and mechanical engineers is a way of thinking. I realize that sounds very woo, but it's very obvious to me and to other mechanical engineers I've spoken to.

As a fellow trained ME, yes, it seems obvious to me as well. A good school and program will have you spending several years in intensive study and thought about the fundamentals and wider implications of the physical principles and mathematics of machines and systems. If you can then follow that up with a few years of good hands-on professional experience with the subject of your study, it's going to give you a level of insight into the workings of the physical world that is difficult to achieve just through direct experience.

Which is not to say that you can't succeed in manufacturing without an engineering degree. It's pretty common for experienced machinists/welders/etc. to break out of a career cul-de-sac and go into business for themselves and engage in some effective and knowledgeable engineering in the process.

But there's no shortcut. You either do the schooling, or you earn the experience. Otherwise, you're not even going to be realizing the mistakes you're making.