What major and school to apply to?

For safeties, I’m largely considering state schools. They’re certainly very good schools, but not selective like UCs or UMich are. Hence, I believe I have a very high chance of getting in.

The reason I said engineering is I have a lot of research work in engineering (electrical and computer engineering specifically) that might give my engineering application a boost. Not taking Math II is one of my regrets, but, alas, there’s not much I can do at this point about that.

Do you think engineering schools are looking for diverse engineers or people who eat, sleep, and breathe STEM? If the latter is the case, I’ll probably go for arts & sciences (though I still think I’d be pretty competent as an engineer).