Is it possible to apply for an ROC ID card *while* still holding an ARC? As in....Can the 270 days be counted retroactively starting the date that I received the ARC or would I have to apply for an ROC passport first, at which time the "one year/270 days for 2 years" rule would apply?
Not sure what you mean by this day count, but since I'm in a similar situation as you (child of Taiwanese parents, born in the US) I'll let you know what I've been told by the National Immigration Agency. Note that this is information from a year ago. Things might've changed since I last asked, but it hasn't in decades and I doubt it has now.
Basically, as far as NIA is concerned, we're both foreigners who also happen to be children of ROC citizens. In the meantime you're only eligible to have an ARC. You have the right to apply for an ROC citizenship, and the ROC ID that comes with it, regardless of your age, but you just can't do it here. It doesn't matter if you are standing in front of an NIA officer in Taiwan with your Taiwanese parents, their documents and your own ready. They just won't do it. My dad tried it when I was 5. I tried again when I returned at 23, and few more times after that. It just couldn't happen.
NIA states that you must apply at your home country. That's right. You must buy a plan ticket, fly back home, halfway around the world, go to your nearest TECO, apply through them, wait as long as it takes to process the paperwork, be issued your ROC passport, and then fly all the way back to re-enter Taiwan with your new passport. It's an enormously time consuming and expensive process. Not sure what your future plans are, but I would think about why you want an ROC ID first, and then consider whether or not it's worth the trouble.