I'd say you'd be fine as long as they actually know you and can write a decent letter - if they write a crummy one it might just look like you're stretching, but don't stress. Especially for the non-core sciences, I think a person with a masters would be fine. And yes, all of the professor letters must be from professors you've taken classes from.
Good luck!
And I LOVE your Sig btw. 🙂