To resolve this, I changed the Proxy module I was using. It uses less code to implement and works with websockets. I think the NodeBB Node.js proxy documentation is out of date so I'll be submitting a PR with the new method I found.
Working code is as follows:
* Proxy forum
const proxy = require('http-proxy-middleware');
// Forum Proxy
Another potential GOTCHA here is that this Prixy setup needs to be declared ABOVE the 'body-parser' module (if it's being used). The wrong order will prevent post requests from being proxied.