[tjr]

Some jobs artificially demand a degree, as in, the HR department will file your application in the garbage if you don't have one. There may be other ways into those jobs, but to a first approximation, you "need" a degree.

And some jobs flat out don't care about degrees, just so long as you can do the work.

You might consider transferring to a different school. Cornell College, for instance, offers a one-class-at-a-time schedule, so you could do your proposed, "study calculus, then study physics" sequence. And Olin College is reputedly very good for teaching engineering-oriented subjects.