I test the same Ternergy battery on the DBS V2 and the light works fine. I think the M2 heat up quickly thus battery shut down.
I'd suspect your batteries aren't holding voltage under load as well as they should. Fully charged, the batteries should read 4.1-4.2 volts each. When the flashlight is turned on, the batteries immediately sag to a voltage of about 3.7 volts each, assuming they're in good condition. When the batteries are worn, they may drop to 3.4 volts are less when the light is turned on. In this case, they'll reach the low-voltage protection threshold of ~2.8V per cell very quickly. I've seen worn batteries that instantly sag to the shutoff voltage in a matter of a couple of minutes. This can happen even though the batteries read normal voltage off the charger. The only true way to determine a batteries state of health is to do a measured discharge.
Ok, with all of the above taken into account, the M2 places a higher load on the batteries than the DBS does. This will cause worn batteries to sag in voltage much more quickly... that's why the batteries appear normal in the DBS... it's just not asking as much from them. Don't misread this as a negative against the M2, it's just due to the fact that the M2 is pushing a lot of current to it's quad-die LED... there's essentially four dies to feed, afterall.
(or three regular LED's in the case of the M2X).
And as far as getting unprotected cells instead, I wouldn't recommend it. Protected cells protect not only against under-voltage, they also protect against over-charge (over-voltage) during recharging, over-current, and short-circuiting (which is also over-current). These are valuable safety features that may well save your house from fire, and save you from injury. Not bad insurance for giving up a couple of bucks and a few minutes of runtime.