We have a winner!
Code:
RewriteEngine On
RewriteCond %{SERVER_PORT} ^80$
RewriteRule ^(.*) https://%{SERVER_NAME}$1 [R,L]
Works like a charm, and even does all the crazy url rewriting I didn't need, so if someone changed their current page, however deep into the app they are, to
http:// it will automagically change it to https.
I googled "apache rewrite http to https" to find it. ("Redirect" was just a bad word I guess, so after trying a few other searches, I finally found something.)