If I remember correctly, you should be eligible for the NWOHR passport, but maybe not TARC (at least under some of the categories for application). This thread might be similar to your case: My mother is NWHOR with supporting documents but her application TARC AF384 was refused by NIA - #5 by Hayashi
If you just want the passport and Chinese name done for heritage purposes, completing the passport part would be enough for that.
TARC would make settling in Taiwan easier, but there are other options for that.
The best thing to do is probably email the NIA in Taiwan with as many specific details as possible.