I figured out the answer to my own question. First I moved the HDMI output cable coming from my monitor 3 (the monitor I was having issues with) from the HDMI 4K port to the standard HDMI port on my external USB to HDMI converter. This alone did not fix the problem, and I'm not sure the step is even necessary. Just mentioning it in case.
The steps that most likely fixed the problem involved using the display configurator found at settings => system => display. Specifically, from within the configurator, I selected monitor 3 then chose "Disconnect this display" from the dropdown menu available in the interface. With monitor 3 still selected, I then chose "Extend desktop to this display" in the same dropdown menu. After that, everything worked.
During the above process, some confusion arose while I was getting the monitors arranged properly in the configurator to match my physical setup. Here the trick was remembering to click on "Apply" after adjusting the virtual monitor arrangement before testing whether Windows "understood" my physical setup. Because of this, it's possible that the only problem I was facing the entire time was failing to click "Apply" before testing the setup. In any case, if you're having a similar problem to mine, try all of the above.
Finally, I get why the monitor configurator dropdown choices are the way they are, but an additional "Extend desktop to all monitors" option would seem to also make sense.