sharky5656

Thank you! I will talk to the installers as I am not supposed to be dealing with this, being just a hobbyist and not a professional! I cannot see any washers and all of the cables  that I have access to, at least, are indeed very tight.
The bad thing about our situation is that space is rather limited and is complicated further by a wooden column that sits between the two batteries, increasing their spacing perhaps needlessly. The inverter is on only one side of the wooden column. I am saying this with respect to the cable lengths. Or maybe there is some way in which the installers could make them equal lengths, we will see.

Thank you very much for the in-depth suggestions, as previously noted, I will talk to our installers and try to figure this out. 
 
This morning, when I looked at the state of the battery after last night's restart, the cells were still out of balance by about 260mV.
 
Hi there! The BMS should be either a Pace BMS or a Gobel BMS (from what I understand, it is something of a rebrand of Pace by Gobel, but I am not sure). The firmware, reported by PBMS tools is P16S150A-21545-1.05, which leads me to believe that the BMS is Pace P16S150A, because I was able to find such a model on Pace's website.
As of now, I feel like the issues are with the BMS itself (or maybe with some of the cells as well), because last night's restart did not make any sense - I find it impossible for the battery to go from 53.2 to 56 volts in a matter of a minute or two without something catching on fire  or maybe I am missing something fundamental in my understanding.

A lot of information here, do you have access to individual cell voltages? This would be the best place to start.
The only way for one battery to discharge into another is if there are voltages differences, SOC differences also hints at this.
Check your cable connections and your DC fuses on the battery line for solid connections and any hint of overheating.
Have you tried using (charge and discharge) the batteries without interbattery communication as well as communication to inverter, just to rule out any communication issue?
Perhaps also try charging then without communication (using LA setting with correct V paramater for you battery) at a modest Amp setting, or manually throttle (aggresively) the amps as the SOC reaches 80%. Let it charge to 100% and leave it for a day or two to get the cells to top balance.
This is all just really a guessing game, you need to see what the individual cells are doing.