This question about displaying equations on the web is similar to what I'm asking but does not answer my question. It's about math. I'm extending that to proofs.
This is a key difference because my main difficulty is formatting issues like adding newlines, and you don't need to worry about those when you're writing isolated math or equations. I'm using MathJax, but any sentences I write are all on the same line because I don't know how to use MathJax to simply insert a newline, and it's surprisingly hard to find.
The play is to use HTML <br>, and the problem I had before doing that was autoescaping HTML. Turning off the autoescape (I happened to be in Django, so that's just {% autoescape off %}{% some_proof %}{% endautoescape %} in the HTML file) and using <br> works exactly as I want and I think is what MathJax expects users to do. So you can write math with MathJax and format the proof with HTML.