If you overview the relevant legislation regarding work permits for foreigners in the ROC, which is the Employment Services Act, you will see that it involves the concept of “fixed employer.”
That may not be specifically stated in the law, but it is indeed inherent in the formulation.
As such, according to the description of activities which you have made in this thread, I don’t see that you actually have a “fixed employer” which would be recognized under Taiwan law.
Hence, unless there is a major legal revolution here or something, where foreigners with residency rights are all given automatic work rights and that sort of civilized treatment, … it seems to me that you are out of luck.
– Richard W. Hartzell