Here's an example of a window I closed on the low DPI display, and then where Firefox appears on next launch.

And one more discovery: if the window on the low DPI display is small enough, it will appear in the same spot on next launch. E.g.:

This might be a problem with hardware acceleration.

You can try to disable hardware acceleration in Firefox.

• Options/Preferences -> General: Performance
  remove checkmark: [ ] "Use recommended performance settings"
  remove checkmark: [ ] "Use hardware acceleration when available"
• https://support.mozilla.org/en-US/kb/performance-settings

Close and restart Firefox after modifying the setting for changes to take effect.

• https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems
• https://support.mozilla.org/en-US/kb/upgrade-graphics-drivers-use-hardware-acceleration

That doesn't seem to have made a difference unfortunately.

It's probably a known issue, see https://bugzilla.mozilla.org/show_bug.cgi?id=1261441

I think you're right.

Note that the bug seems to be about 32-bit Firefox.

Did you close and rstart Firefox after modifying hardware acceleration?

Does resizing the Firefox window or using the system menu (Alt+space) work?

Yes, I did close and restart Firefox after disabling hardware acceleration.

I can successfully resize the window after it launches partially offscreen, and like the bug report linked above notes, if I resize the window onto the second screen it snaps to a smaller size with the menubar visible. The issue is just with where the window appears on launch.