If two of the main drivers for the battery are APU start and brakes, why wasn't air considered?
I know the spec. for APU starts required the capability of multiple re-starts up to and including service ceiling (43k) but multiple could be any number between 3 and infinity.
There is also the possibility of having a hybrid braking system, electric on the front axle of the main gear and pneumatic on the rear axle.
Accepted, there are potential weight penalties but you've also introduced additional redundancy to the braking system