I had a call with @warwickchapman from Sensible Solar - they are awesome by the way 
He suggested disabling vsense in the MultiPlus, which does not make much sense since I did not even have a vsense cable installed. But what do you know - this fixes the inaccurate voltage reading and the repeated charging / discharging when the battery is 100 % full.
I did a bit of searching, and also found this thread: https://community.victronenergy.com/questions/196650/why-is-mppt-reporting-nearly-3v-higher-than-pylont.html
Guy Stewart made a post in that thread that was related:
This is my system diagnostics page before disabling vsense - you can see the “sense” voltage is far from the terminal voltage.
After disabling vsense:
Bus voltages after disabling vsense:
The oscillation of charge / discharge when the battery is at 100 % has now completely stopped.
It appears there is something wrong with the vsense hardware / algorithm in my MPII, and this affects the voltage reported by the MPII even if you don’t have it connected. It does not matter too much since I have a LiFEPO4 battery with BMS though.