Hy Rorut,
Nice informative post.You can see the echos of English is your translation of Swedish.
You say that you have four Panasonic NCR3400 batteries, but I cant find that part number. Did you mean NCR18650B?
I ask, because one of the critical areas to get right in a cut off circuit is battery rebound, and this depends on the load (last) and the battery characteristics.
Basically, without the correct window (hysteresis), the cutoff circuit will oscillate: on load the battery voltage drops to 3.5V and the cut off circuit activates and removes the load. This causes the battery voltage to rise and the cut off circuit reconnects the load and so the cycle continues.
Rebound is not significant for very light loads, as in the real time clock back up battery cut off circuit I did recently on ETO, (
https://www.electro-tech-online.com/threads/help-with-backup-circuit-for-digital-clock.147727/ ) but in your case, rebound will be significant.
spec