Pulling together random snippets that lie around the internet, I know that it's possible to build a textarea auto-indent. So I did.
It is based off of the somewhat incomplete jquery extension at http://laboratorium.0xab.cd/jquery/fieldselection/0.2.3-test/. I haven't decided if I will turn this into a jquery extension, and I haven't decided if I'm going to try to make it work in IE.
Check out the jquery autoindent demo!