Why on earth do you want to use 2x14500 instead of 1x18650 if you want to run on li ion? A good 18650 has almost 4x the energy capacity of a 14500, is quite a bit shorter than 2x14500, and it can run either of the Quark heads at full brightness.
I've always been leery of 14500's because I figure if I used them in anything, I would eventually put them in the wrong device and end up burning out something that expected normal AA's. It sounds like that is what has happened here. If you have the low voltage head and the 2aa tube and want to use rechargeables, the setup should run fine on two 1.2 volt NiMH cells.
It would sure be nice though if 4x7 could make a Quark head with true universal voltage, everything from 1 volt to 9 volts, instead of having separate low and high voltage heads. The turbo head in particular is fairly large and could presumably accomodate extra electronics. That would get rid of this whole problem.