I think Selfbuilt’s video review is the pre-production version. The production version is a revised 02 and has a constant-current circuit design for constant output, among others.
Some quick and dirty calculations, please correct me on mistakes: The MT-G2 has a Vf that is about 6.5 V at 4A current (this is my led-current guess in this flashlight), various resistances in the flaslight eat say 0.3V, the driver may eat another 0.1V so two batteries in series must deliver 6.9V under load. A popular Li-ion (Panasonic NCR18650B Protected 3400mAh) under 0.5x4=2A (there are two series, so 2A per serie) load stays over 6.9:2=3.45V for over 50 minutes.
So I'd say yes, a driver can be be had that keeps the light in regulation for quite some time.
I’m not trying to be obtuse, but I must be missing something. Their website doesn’t say anything about changes from the versions Selfbuilt tested. Yes, it lists constant current as a feature, but that doesn’t mean it really has it in the sense the FA01 does, or that the shipping FA02 is going to perform differently from the one Selfbuilt reviewed.