I hate telling people to do things, and them find out it helps little. I do feel so bad for your problem, I have one person have success with this fix and another only a small improvement.
Recharge the battery to full and leave stand for a while.
Then set the timer to switch off after 30 mins and on after an hour rest. If you notice it only stays on full charge for a small time when you switch it back on, this means we are not getting the high cells down enough extend the rest to 2 hours..
What you want to see after you rest the battery from the charge is bulk charge going in for some time. Even 15 minutes is awesome. If it goes on for 15 mins then switches off automatically Then you can make it go on for 20 mins and off for an hour..
Let me explain why this can work. If the cells are way out of balance. What can happen is a few cells can reach full charge while 1 or two can still be undercharged. If a few full cell reaches 3.8v LFP or higher than 4.2v LiMn the the charger reaches max volts and stops all the other cells getting a charge, in order to protect the high cells being damaged.
This can indeed happen with self discharge over a long period and a runt cell. The battery can still work fine with a runt cell, but a runt cell can lose voltage a lot faster than the other cells over a long time.. Moisture on the
BMS can also plague a pack to unbalance during long term storages.
When a high cell reaches 3.65v LiFePo4 the
BMS also switches a resistor across the cells terminals, to keep it from over charging. Some charges will not allow the cell to drop from this voltage if they stay plugged in, and the charge can provide enough hold voltage to keep them high. When you switch the charger off, this resistor over all the high cells brings the voltage down over them much faster thus taking the whole pack voltage down to not reading a full charge again. When you switch the charger back on the charger hopefully will go back into full charge mode and give any low cells another decent hit of current, because the resistor has not switched over the low cells, they are not discharged by the
BMS, so they start to regain capacity every time the timer turns the charger back on...
So we do this on-off timer thing, over and over, until the charger no longer goes to bulk mode charge rate after the rest period, and this is the indication that you've come to your end. Try the pack out if you get 30+ kms down the road, then we won here.