It could be related to battery position, rather than purely electrical characteristics. The spaces for AA and AAA appear to be keyed for the cell diameter. Since everything is the same, electrically, except for the mAh, you can probably control the LED driver by using basic position sensing on the cell locations with minimal components and efficiency cost. An LTC3090, for example, could be used with relatively simple voltage dividers to adjust the ratio on the Vin and Vctl pins.
It could be related to battery position, rather than purely electrical characteristics. The spaces for AA and AAA appear to be keyed for the cell diameter. Since everything is the same, electrically, except for the mAh, you can probably control the LED driver by using basic position sensing on the cell locations with minimal components and efficiency cost. An LTC3090, for example, could be used with relatively simple voltage dividers to adjust the ratio on the Vin and Vctl pins.