Rockworm
I've thought of your idea, as I'm sure many others have.
The dimmer part of the battery pack looks like it could be
cut (sawed) off the 3 aaa holder and then epoxied on to a 3 AA battery
holder.
As a test measure the current out of 3 new aaa batteries into the
H7 on full blast. Then before cutting anything jumper wire the 3 AA
battery holder to the contacts in the 3 aaa holder and again
measure the curent on full. (remove 3 aaa batteries first of course)
Should be similar values if new cells are used for both tests
..and same battery type chemistry ie NimH , alkaline, lithium).