If I was the OP I would be a right a*shole (after them denying my request to submit an application several times which will inevitably happen) to the NIA staff until they submit the application to the actual A(P)RC approvers, whoever they may be.
Downside - $10,000 fee and possible rejection.
Naturalisation is cheaper and in my experience the Household Registration staff are smarter (but not by much) than the NIA staff. He could even convince the Household Registration office to submit an application and just wait to hear back from the MOI
Either way, I think the OPs best option is to make sure an application is submitted somewhere then wait and see what happens
Where do you live? iiuc, a foreign parent who actually supports kids and excises the right and obligation as a parent or has visitation right can be allowed to stay even if the parent doesn’t have a custody. If it is in Taipei or New Taipei, they might have given an extension.
Naturalisation is a dangerous thing, and I’ll explain why.
The UK does everything in its power to make it harder to emigrate there or get citizenship, and because I have my aging father there plus major assets, renouncing my British citizenship would be playing with fire. Getting a Taiwan passport at the expense of my British one is out of the question.
I’m going to attempt to get custody, which means a family-dependent ARC. As I say, that ex-wife is not exactly on favourable terms with me, but I hold some power, which isn’t just with money… some of her valuables are still in my apartment for safekeeping, which I will throw out if there’s any trouble.
your copy of your declaration of renunciation (either form RN1 or R6)
your passport, or certificate of naturalisation or registration for your current citizenship or nationality
an official letter or statement from the country you’re currently a citizen or national of saying that if you had not given up your British citizenship you’d have lost or failed to get your current citizenship or nationality
Can I also add that my dad is in his 70s now, so if GOD FORBID anything happens when I’m out here I must go back immediately to deal with everything. That’s why it would be completely reckless to pursue naturalisation with this policy of giving up your birth citizenship.
Did you already ask to the headquarters of NIA in Taipei? If not, you could ask them a few times by email and phone. Different personnels could say different things. you could also ask them what is the legal basis of the answer they would give you.