We also went to AAA to get international driving permits (no test required) that will allow us to drive for 6 months before we get Taiwanese driving licenses. Side note: I would not recommend Walgreens for passport photos.
Finally, today we drove up to the Taipei Economic and Cultural Representative Office in Seattle to sort out our resident visas. We could have done it through the mail, but the process was a little confusing and the website no help at all. Screwing up our visas was not something we wanted to risk and the drive was pretty quick. Once there we each filled out a form, wrote a check and handed over our passports. They will mail it all back to us in a few days.