Does HTTPS Everywhere actually work for you? It's utterly useless for me as far as I can tell. Try going to some site (say, example.net) in Chrome and watch it just load HTTP.
IIRC, you have to enable the "strict" mode, or something along those lines, in the settings before it rejects HTTP connections from being made. I had the same issue.
Thanks, but then what do I do about HTTP-only sites? Why can't it default to HTTPS and then auto-fallback to HTTP when HTTPS connections fail for sites that aren't in the known-HTTPS list? It seems like a logical thing to do instead of just going straight to HTTP.