Apparently, there are few tools (if any) that do this (at least that I was able to find). I've found a way to do this by writing a script that hijacks the window event loop and stores all the input values in a stringified cookie. When you refresh the page, you can use window.onload to automatically repopulate the inputs.
If you (understandably) don't want to write your own script to do this, I've written one you are welcome to use on github.