Hi Larry,
Welcome to Taiwan. Just thinking outside the box a little…
1/ On visa, I see you have a degree in Environmental studies, and work as a budget analyst. Is your degree related to the government department in which you work? If so, do think you could claim 5 years of expertise as a ‘financial professional in green energy technology’? Or, do you think you could arrange a collection of documents that could sell your professional talents as being outstanding/in demand in Taiwan? Or, is your salary more than about USD 62,500 (current exchange rate for 160k TWD/mo)?
If so, you might be eligible for the Employment Gold Card four-in-one visa. It comes with an open work permit, which could simplify your immigration and job-hunting process substantially. There’s a thread on the forum and my own little blog post.
2/ An alternative to finding teaching work is to see if you can arrange a ‘remote’ job. That is, work ‘from home’ for a US (or other country) employer while being based in Taiwan. The advantages are that you can use your existing professional network in US to find such a job, it’s likely to be a higher salary than what you could get teaching, you can continue to use your professional skills and it still comes with greater flexibility for work-life balance. The disadvantages are that they’re not easy to find, and you need to pay some extra attention to tax and visa issues.