Weird Stefan.
My best guess, based on above information, is that AO has a mismatch between the hostname in the CSS/JS-url and the hostname in the URL returned by content_url(), in which case AO does not aggregate the JS/CSS as it considers the file not to be local.
More specifically I would suspect "I'm using the HTTPS plugin because everything is HTTPS" might point to the culprit causing the mismatch. Could it be you don't have that on your local installation? Can you -briefly- try with the HTTPS-plugin disabled?