Don't try to do it via NSMutableURLRequest & setValue:forHTTPHeaderField:, doesn't work, UIWebView overwrites it.
When UIWebView will be replaced with WKWebView (in Pythonista), it will be much easier because of customUserAgent property.
Thanks for looking at my code. I'm glad to know I hadn't overlooked something silly.
As it is, I am trying to make an extension to re-display or mobilize certain kinds of websites. Imagine if I went to a website full of thumbnails, and the script grabbed all of the linked full-size images. There's other websites and whatnot, but I was mostly playing around with extensions for now.