Without.
@andrew beat me again. I gotta stop letting girls distract me from my phone!
You can also just fly to the Philippines for a short vacation (one day is enough) and come back to Taiwan with a new 90 days. Some people have lived like this for years in Taiwan. Not sure about flying and pregancy. Consider spending a little down time in the PH. Some very beautiful relaxing places/beaches. Try Ticao Island resort for good value.
You might also consider the Employment Seeking visa. I believe it can be extended for six months giving you a year. But double check.
Is it possible that you get a Gold Card? Their online chat service under Resources can be very helpful.
Internships are another possiblity. You obviously need to find a sponsor but they can be up to a year and pretty flexibile. Some NGOs sponsor internships.
Good luck!