Aha!
C:/Users/<your user>/AppData/Romaing/Esri/ArcGISPro_StrongName_<someid>/3.2.0.0/user.config
<setting name="MainWindowPlacement" serializeAs="String">
<value>WP|0|1|-32000|-32000|-1|-1|1920|0|3390|1032</value>
</setting>
Somehow, these values do not correspond to the monitor arrangement, resolution, etc., but this was the setting being used to open the application to a specific position.
I'm not positive how this string is being interpreted, but it seems it was using 1920,0 and 3390,1032 as the corners. That would make the lower-left corner of the application outside of my monitor's range, and extending further right from there.
Messing the the values to get them in a normal range brought it back to reality, then closing the program updated this line of the config.
WP|2|3|-1|-1|-1|-1|-2131|227|-1995|1027
Really not sure where the previous values came from, as I have used Pro on the same machine and made no display changes since then. But at least it can be fixed!
- Josh Carlson
Kendall County GIS