A big insurer on the West Coast can do the test and get the result back in 12-24 hours.
Check your insurance provider.
Tell them exactly why you need it and the urgency.
If you do not have an insurer, then google galore and find some clinic near you that guarantees a result within 24/36 hours. Tell them why you need it. Many Americans need to get Covid-19 test before flying to Alaska, so it is not unheard of.
As for the 3-day window, it is not the “tester” that is the problem, but the lab where the tester/ sends the test to. If the lab (which is apart from the clinic/hospital) has a huge overload of cases to test, then yes, it may influence when your result gets back.
If you do need the 3-day test, then here’s how Taiwan government calculates it.
For example, your flight takes off sometime on July 14 (does Not matter what time of day). Taiwan government will not include that day in calculation. It will work backward from then for 3 full days. So, the “earliest” you can take the test would be starting 12:01a.m. on July 11.
Call up Eva Air staff (NOT the toll-free booking agent) at a West Coast airport. Try this number after 6pm West Coast time: 206 242 6868. They should confirm this (again, if in fact, you need that 3-day window).
Make sure the negative test certificate has the clinic with some doctor’s signature on it and better yet, in color.
Good luck