I added a special case in my code for "device manufacturer = OnePlus", forcing "has no menu key, need the three dots".
I'll test it as soon as it will be available.
I hope I'm slowly getting the terminology right (Action bar, Menu icon vs. Overflow icon).
The settings for message view has a submenu with long list of buttons, which can be optionally displayed on the bottom "button" bar. Could this list contain also the triple-dot menu button?
No, the triple-dot overflow icon is not a "real" action icon, it's just an icon to get access to any other action commands that didn't make it as icons in the action bar itself.
Maybe a more arbitrary solution would indeed be to add the "menu button" option to the mentioned button list. Although not being a real button, it behaves so (pressing it causes any not displayed buttons to appear as list of actions), it would logically fit in there and could act as the mentioned "device manufacturer = OnePlus" override, but for any phone with such issue.
Sent from a touch display, which took care of perfectly scrambling my thoughts.