Aren't rechargeable CR123A actually LiFePO4?
3.7V off the charger, rests about 3.4V, and nominally 3.2V.
P60 draws 1.13A, so I think that will work safely, and shouldn't blow the lamp on rested cells. Need to look at the specs of whatever particular cells you're looking at... AW Blue, likely, but those are all gone, right? Have to have some idea of the voltage of two cells under load, and off the top of my head, I have no idea. Rechargeable CR123A bother me because the specs are buried. If sold as LFE16340, then we immediately know what they are. fivemega's input will give security and be definitive.