From your basic description, it sounds like you are underwired and getting too much Voltage Drop / Sag.
LFP like any other battery will take a voltage drop or sag relative to the demand placed on the battery pack. For example, when I run my coffee maker (60A on 24V system) it will pull down the battery bank by 0.4V while it's brewing. My Microwave pulls 80A off 24V and causes a 0.5V sag while running, lead does it too but you have to be watching to see it.
The 280AH cells can output at 1C rate which is 280A and they can even handle a short surge of 5C. Your BMS' would never allow it.
At exactly 12.0V that is 3.0V per cell (12V config) At exactly 14.6V you are at 100%SOC - 3.65V per cell.
LFP working Voltage Curve is 3.000-3.400 or 12.0V-13.6V, anything above/below those voltages is not really significant AH.
Two battery packs in proper parallel could theoretically output a combined 560A because in Parallel they should divide the load evenly, just as when charging the batteries. Your description of Series & Parallel is confusing...
Batteries in Series increase Voltage but not AH Capacity. 12V/280AH+12V/280AH in series = 24V/280AH.
Batteries in Parallel Increase Capacity in AH but NOT Voltage. 12V/280 + 12V/280AH in Parallel= 12V/560AH.
Each BMS is a 150A Max Output which represents 1800W (uncorrected for efficiency) to an Inverter. That equates to 120V/15A from an Inverter.
Ideally, you should have all 4 battery packs set in Parallel. Each battery pack wired to a Common DC Busbar using at least 2/0 or better 3/0 Fine Copper Cable (Royal Excelene is one of the best out there, amperage table below) Solar & Inverter should run to/from that DC Bus. The Inverter Wire should be equal to or greater than the size of cable used from Batt Posts to Busbar. *Each battery should be fused at 200A to 250A. Then feed your 12V system from that BusBar as well.
If wires get Warm but not hot, that is an indicator of resistance which is not good, as it drops voltage. The hotter it gets the more resistance is there, if it get's "hot" then it is dangerous. Check along your wiring, terminals & connections when things are running, if you feel warmth, not too warm is ok BUT if you come across something HOT you may have a poor/week connection, broken wire, or damaged insulation. Even a loose connection on one battery cell Busbar connection will chuck in a pile of issues. It does not take much. Even burrs & Ridges on battery busbars cause all sorts of issues that people chase for days because it's too obvious & simple and many skip that part of the "Required Prep". This is why I wrote the Luyuan LiFePo4 Basic Guide but not everyone looks at it and continue to repeat many mistakes. It's even in my signature to make it easy for folks to find. Imagine That.
Luyuan Tech Basic Lifepo4 Guide
Remember for every 1000W to a 12V Inverter, it requires 84A and do not forget to consider Surge Capacity.
Hope this helps you, Good Luck
Steve
