So.... My best guess is about 1200~1500mA range at the time of cut off.
The PCB looks at voltage AT THE TIME it activates a protective mode. Not when you test it after the fact.
Under a strenuous load, a LiCo cell can be expected to suffer from significant voltage sag. The 2.5V bottom end limit of the PCB was reached, the load was removed, and the cells resting voltage rebounded to 3.4V....
FYI: anything between 2.5V and 3.5V resting is basically dead, the difference is, at 2.5V it's dead as a freaking doornail and ideally should be charged to a higher level ASAP to reduce wear-and-tear on the cell, at 3.5V you can let the cell sit around for awhile before you get to charging it and not take much penalty on cell capacity/life.
It doesn't sound like there is anything wrong with your cells.
What you'll tend to find is this:
When you have a pair of li-ion cells driving a buck regulated LED, or a single cell driving a boost and or boost/bucked LED, the current draw from the battery will rise towards the end of the discharge, which causes there to be a large gap between resting voltage and running voltage at the cell, especially towards the bottom end of the cycle.
When you have a single li-ion cell driving a LED in a buck regulated or direct-drive configuration, the current drops lower and lower towards the end of the discharge, which causes the gap between resting voltage and running voltage to stay very narrow right down to the very end of the discharge.
Some 1xli-ion "drivers" for LEDs will also start to really wane off on the boosting towards the end of the discharge, which offers some extended running at a lower output, but will also cause deeper slower discharges with lower final resting voltages at the cell.
-Eric