You can run your pack as it is but must have the BMS operational to protect it. You wont have full capacity but it wont be too far off. Set the charge voltages in the solar chargers or any other charger to a maximum just below the point where the high cell reaches the limit, with 3.65 in the screen shot you gave, that would be 13.7 volts. The balancing feature in the BMS will, slowly over time, get things more in balance, so you could increase the charge voltage as necessary.
Using the pack imbalanced is not ideal but gives you a usable solution, provided the maximum charge voltages are set appropriately and any float value is 13.4 or less.
If the settings in the BMS are adjustable, set the pack maximum volts to 13.8. , minimum to 12.0, cell maximum to 3.7, cell minimum to 2.8. As you get the pack more in balance increase the pack maximum, so the highest cell still stays within 3.65, when balance complete set to 14.6.
With the pack assembled and charging near the high limits you can manually balance by draining power from the high cells one at a time or by adding power to the low cell. Its not that difficult to do with a 4 cell battery.
(Note I use the term cell for the cell group of 4 that you have in parallel). Take the usual safety precautions when working on the battery and take care to avoid accidental shorting.
Make up a suitable load, 12v bulbs wired in parallel to give about 50 watts, a 12v DC soldering iron, or anything else that will give a load 20 to 100 watts at 12v. Use suitable leads with a small contact area you can manually attach to the buss bars in the battery, you will be holding in place for several seconds. It just needs hand pressure , not bolted or clamped.
Taking the screen shot you posted as an example, cell 1 is high compared to 2,3,4. Whilst monitoring the cell voltages put your load across the cell for a few seconds, repeat as necessary varying the time. With a little experience it becomes easier. Once you get cell 1 voltage to match the rest, one of them will take the lead , say cell 3, so work on this cell with the load, to pull its voltage down to near the others.
It takes a little practice as the cell volts ' jump up' somewhat when the load is removed.
Once things are near enough, say 30mV differential and remaining steady under charge, increase the charge voltage in stages, repeating the 'balance' as necessary. It will work, it may take some time, but as you gain experience with the 'contact time' and its effect on cell volts, the process speeds up.
Since you have four 120Ah cells in parallel making up one 'cell' in the battery, these will self balance over time but may affect the 'cell' balance in the battery. Hopefully the BMS and the initial random selection of cells to make up the parallel group will minimize any effect. If it appears the pack is going out of balance you may need to repeat the manual balance procedure.
I recommend you check the cell volts readout as given with the BMS with the voltage given with a meter. Its not uncommon for errors.
As an alternative you could use one of the solar panels directly (no solar regulator) as a 'constant current charger' on a low cell to add power and raise that cell voltage. Again it requires a temporary connection to the buss bars. Unlike the 'bleed off' method the panel is polarity sensitive so a series diode would be useful.
The two techniques are similar methods of obtaining balance as outlined by smoothJoey but using items you already have.
Mike
