By the way, I did as I told, and this FP2 is now running the latest official Android7-based release of Fairphone OpenOS (fp2-sibon-19.11.2-manual-v2).
So far, it works extremely well: there’s no issue I can see with either the battery or the display. The UI responds correctly to touches, and all indicators reflect the real hardware status (WiFi on/off…). 4G connectivity works well (web page in FF Klar), as do the USB-charging and data transfers.
The only minor hiccup I can see is the apparent inability of DAVx⁵ to sync over 4G, but sync over WiFi is OK.
As it happens, I also have a similar issue on my LineageOS 17.1-based FP2, except the culprit is ICSx⁵ for me…
Well, end of the story 
Thanks all for your great and quick help!