There you go!
Equal voltages doesn't mean balanced. It mean equal voltages. BALANCE refers to all cells being at the same state of charge. The only time you can be 100% certain of the state of charge of a cell is at full, 3.65V or empty, 2.5V. Equal voltages in the operating range of the cells tells you nothing.
A "balanced" battery typically means that all cells are at the same state of charge when the battery is charged to 100% SoC.
Now you know why you can't charge higher. You have runners due to many cells being at different states of charge. They probably aren't that far off - probably not more than the 1% mentioned earlier in the thread.
Simply charging and discharging is going to take forever to balance them. You need to hold the pack at the lowest voltage that will still accept current and enable balancing of the high cells.