In Taiwan on visa-exempt US passport, what are my options

Check back in 30 days. There’s no doubt a big rush on MOFA/BOCA offices but that should subside.

I’m going to assume that limited flights around Asia will resume by early May, as Asia is no longer the epicenter of the problem.

If things don’t look good in two weeks consider incorporating a shell company in Delaware and setting up a rep office

That will allow you to get an ARC and pay yourself here. It’s a totally legit way of doing it too; I know a bunch of people that have this kind of set up. If you can speak Chinese you can get an accountant to do most of the leg work for you for 5k NTD