The main issue is weight. A 6-cell, 270mAh NiCd is about the heaviest battery you'd want to haul around with this plane, and still have it flyable. 950/1050 NiMH, even if only 6 cells, are about twice as heavy as the 270mAh NiCd. The plane won't fly well at all with this much weight, and you'll probably fold the wing.

You're correct in your understanding that mAh really only affects duration. Cell count, which is what determines voltage, is what controls the power. If you use more than 6 cells, you will be pushing too much power through the motor on this plane with the stock propeller.