I’m not entirely sure about the rules regarding extending a visitor Visa. I had to do it once and I I needed to show proof of why I needed an extension. In hindsight, it would have been a lot easier to have a multiple entry visa and just fly to Hong Kong and back.
I messed up our jfrv in every way possible. Taiwanese bureaucracy is a pain to deal with. Be prepared for that. But as long as you know that you’ll be together forever, and you’re patient enough and willing to wait forever for all the paperwork to come through it’ll work out eventually :-).