I would like to correct what i've said. There's a reason 1aa lights are really popular or mass marketed.
Sorry, the more i've thought about this, the more i'd like to ask what gave you the 1aa requirement. There's only so much power in that cell and it will really limit output / runtime of any light you get...I was thinking you might be able to upgrade an emittor if you find a nice host that uses an outdated led. While it is possible to regulate a light to boost output for you (your stated use - many brief activations during a day dive), I can't do this and can't recommend anyone who'd take this on.
Think about it; there's lots of lights out there, and lots of modifications in here. My suggestion is to look around / wait around for someone to offer what you're looking for.
Of course, you are also totally correct to request someone make something for you, just my $0.02 that you wait around a bit first.
The single AA or AAA requirement simply comes from form factor. I've always subscribed to the less is more philosophy, especially while diving. I'm a pretty relaxed diver... I move slowly and like to check out nooks and crannies. I want something that I can grab quickly and easily without the need for lanyards, clips, or zippers to undo. I would like something small enough to secure it to my BC with a strip of velcro, making it readily available without the fumbling around with BC pockets and clips. It would
not be used as a backup light (I always carry a UK SL4 in my BC pocket as a backup), so if it did end up getting knocked off and lost it wouldn't put me in a critical situation.
I do a lot of underwater photography, but I like using a little point-n-shoot without an external strobe because I like to wedge my camera in small crevices and under rocks to get the little creepy-crawlies and shy creatures that inhabit tight spaces. With a single AA or AAA light I could also attach it to the side of my camera case (again, with velcro) and use it as a spotting light.
Now, like I said earlier, I do have a Q40, but with 4xAA it's simply to big to attach securely with velcro and too large to attach to the camera case comfortably. It can clip to my mask strap, but that doesn't allow me to get the light right where I want it. I either keep it secured to my BC with a retractable lanyard or with a clip, but I hate how it flops around as I dive and it always seems to get stuck behind a pocket or under a strap whenever I really want a light as quickly as possible. In addition, its length causes it to get tangled with my compass, camera, or whatever else that I have hanging off of me at any given time. The end result is that I don't use it very much because I don't like the hassle of getting it at the ready.
I guess what I am looking for is something that fulfills the same role as the 1xAAA light that I carry in my pocket. I use my pocket light all the time because it's so quick and easy to pull out and use. It doesn't
replace the larger lights that I carry in my backpack or glovebox, but it's availability makes it so convenient to use that I grab it in a lot of situations in which I would otherwise say "forget it"