I have never looked into bringing parents to Taiwan as dependents so can't comment - looks like a dead end.
What I can suggest is opening Labuan Company with USD65K+ will give you 2 year renewable business visa for applicant/spouse + dependents (under 21) + parents of main applicant with permit to reside in Malaysia.
Have your folks look into Malaysia. Flight to KL from TPE is 4.5 hours vs. 9 hours to BNE. Cost is USD200 return vs USD700 return. Apartments are affordable and much nicer than Taiwan. Yield on KL real estate is better. I know Taiwanese who buy in KL, and rent in Taipei.
KL is great. Food is excellent. English is spoken everywhere. Have Common Law system. Folks can live comfortably and frugally. South East Asia is at your door step. My wife doesn't like KL, so we can't do it unfortunately. Taiwan is closer to China, so Taiwan is more practical for my work.
My main point is there are alternatives if one looks around.
I am a "dependent" in Taiwan, and I am not legally permitted to work. There was a time when I would consider opening a company in Taiwan, but policies make it so hard (common theme on this bulletin board) and it's more beneficial to do so elsewhere. I found a solution that works for my situation.
You could consider registering your business in Hong Kong for tax purposes. I am not clear about the requirements for supporting residency in HK.
You are in an exceptional situation since your family business allows you to work remotely. Use this to your advantage. (full disclosure - I don't like Brisbane...at all) As I wrote, look for alternatives.
Keep us up to date with your decision. Good Luck.