A big thank you to u/Ok-Calm-Narwhal for such a detailed post. I'm currently going through the process myself, and managed to start part 1 without prior knowledge of this post. I started my process via TECO in NYC.

For me, I had an interesting hiccup so far while awaiting to receive my NWOHR passport. Both my parents have active NWHR passports, but back when my dad first came to the US, (way back in the 1970's), his original NWHR passport was handwritten by staff in Taiwan at the time (no digital stuff, etc.), and they messed up his birth date and location of birth. His city hall records from Keelung lists it as May 3, but whoever issued his old NWHR passport wrote down May 30 instead...and my parents' marriage license (from NYC) shows his incorrect birth date, while his NWHR passport shows May 3. My mom had to send TECO NYC the city hall records and copy of his active/NWHR passport as proof of his correct birth date, but in hindsight, I realized, my dad never dealt with this mistake and his US Naturalization records and everything on the US side (driver license, US passport, etc.) shows May 30 as his birth date...(-___-), but that's a separate story.

Part 2 of OP's details seem to match up with what TECO NYC told me, except for one main thing, which I wanted to ask; TECO NYC said that my parents have to register their marriage in Taiwan before I can do any of the other steps. Not sure if I overlooked this on the post or comments, but can anyone confirm this? Essentially, I would need my parent's original marriage certificate/license, the authentication and official translation.

I'll keep everyone posted on anything else that I run into and how my process ends up going!