It's probably worthy of an experiment. I can think of some things to maybe consider.
-Yes, you'd get half the runtime.
-6 AA NiMHs is maybe 7.5v. It's not clear to me if the lighthead itself has any minimum voltage shutoff to protect the powerpack from overdischarge (or if it's in the battery pack circuit). If so, it's probably nearly 7v, IIRC. If your NiMH pack has some resistance between each cell, and they start to sag near 1volt each, you might be out of light, or get a stepdown.
-The NiMH pack - I don't know of any good holders with low resistance and easy changeout. The resistance of the springs in common holders is a big problem.
-You could try a 6P2S pack (2 parallel stacks of 6 series) for more current. Bigger and heavier than the LiIon, tho.
-Maybe consider 7 in series, but the max voltage (maybe about 9.8v fresh off the charger) might be too high for the MS head regulator board (maybe designed with 8.4v max in mind).