That said, it's pretty hard to build a responsive web app without at least a little bit of JavaScript.

Not really. You just need to learn the difference between width and max-width.
I do UserCSS now and then and 2 of 3 sites use them wrong. That and position: fixed overuse. Also, use @media (min-width) only for layout changes, not for sizing.

And also, functionality/layouting first, design after.