With fresh batteries measuring 4.20 volts unloaded I get 3.87 volts volts loaded with a 14500 and 3.94 with an 18650 (510 atty). I did checks with a 510 passthrough some time back. It drops around half a volt in the wires from the battery to the atty. I doubt if the FET is dropping a lot of voltage - I have used small FETs in a couple of my mods and measure the drop as 0.04 volts.
That's odd. I've been unable to find a 14500 that can properly push a 510. The voltage drop has always been substantial. I've even removed the battery protection pcb to take it out of the equation and always get the same results.