This is just theory based on my observations at this point and me being a bit cautious.
One could ask when they go next if they could whip something up (e.g. the first dish I suggested which is well within reason and in the same culinary sphere) and even the others I suggested, but experience dictates that it’s easier to at least start requesting things that the chef is already doing first, figure out what else he (or she) can cook and is good at, and then gauge as you go.
There is no doubt they could do something off menu that is great and homey, but what is considered home cooked in regional Taiwanese could differ a bit from county to county in Taiwan…Hakka Taiwanese, Fujian Taiwanese (the bulk of the population in the Central and South presumably, indigenous tribes/aborigines, Islamic Chinese residing in Taiwan, buddhist vegans [don’t know what the regional differences in this niche are], military village cuisine with roots from Shandong, Sichuan etc, and of course a medley of everything else in between. And this is not even mentioning the various local ingredients, produce, livestock, and vegetables/fruits. It’s almost as diverse, widespread, and complex like in Japan to an extent. Interesting stuff to geek out on.