if you find yourself on a site directly that you want to view proxied, you can right-click on the connector toolbar icon and choose Reload via Proxy, which will reload the site and add it to the proxy entry.
It's a new feature, and we're going to put up a post about it, but we're waiting until it's available in Safari, and we're also going to try to make a change to avoid the problem you pointed out. That's from only have an HTTP proxy entry and not an HTTPS entry. Currently, you need both for it to work on all sites. (If you create an HTTPS proxy manually, make sure you enable the hyphen option.)
That basically already exists — when you're redirected via a proxy, you get a notification bar with a "Don’t Proxy This Site” option, which removes the host entry and reloads the site. That's really the cleanest place to handle that. Reloading without the proxy while leaving the host entry in place would probably be a lot more complicated technically, and I'm not totally sure why one would need it.
I occasionally found my institution proxy would butcher specific pages on a site, but not the domain generally. Sometimes the issues were intermittent. Would have been nice to have an easy way to temporarily disable the proxy in such situations.
http://www.jstor.org/stable/pdf/1163741.pdf?seq=1#page_scan_tab_contents
but not on
https://www.economist.com/news/americas/21731972-questions-about-integrity-vote-count-will-not-go-away-analysing-juan-orlando