How to get Night Shift on both external monitors?

As the linked answers mention, disabling + re-enabling Night Shift seems to make things work fine. That said...

My guess is that "Night Shift" works by modifying the display profiles for monitors (certainly works that way for f.lux, you can see the display profile change in System Preferences). This happens on my system, and my suspicion is that I have two monitors with the same name (and EDID info, which is probably the actual identifier) => macOS can't figure out that both monitors are supposed to get the display profiles updated, and only one works correctly.

screenshot of doubled Display profiles