So after doing some more digging and asking for help on other forums, I figured out what the issue was with my fare search on Chase, described above. Initially, I had selected economy flights, nonstop, sort by price. The only option was the $1900+ flight on BR (only BR and China Airlines/CI fly nonstop JFK-TPE, and CI doesn't do so daily). That was a mix-and-match fare, with the price at $1900+ as shown above.

However, when I went into the long menu on the left side of the screen that lets you refine the search, and I clicked "hide mix-and-match fares," the portal repriced the same BR flights to $1293. So for some weird reason, it was ignoring the regular cheap fare and constructing a higher fare out of the same flights.

Even more weirdly, after I hid the mix-and-match fares initially, I deselected that option and reran the same search, with the exact same settings I had initially. NOW the $1293 flight does in fact appear.

Does anyone have any idea why this would happen? Unless I'm missing something, it seems like a glitch with the Chase portal - which doesn't give me any confidence in their technology.