"A single AAA light just isn't quite enough when it's dark 14+ hours a day..."
Depends on how you look at it. The EOS lasts approx 3x longer than the LD01, but it also has 3x the batteries (these are vague estimates). So in terms of efficiency it's really a question of whether you want to store the batteries inside the light or outside, and how often you like to swap out batteries in the dark.
For a multi-hour hike in the dark, I agree the EOS is the way to go. But I have found that, for most of my 3-season trips I am in camp before nightfall, and so I felt I wasn't getting enough use out of the EOS. I'd use it for a few minutes here and there. Problem is I'd end up starting a hike with half of the battery left, and so I'd need to bring 3 extra as backup. Or, if I've got a longer trip, I'd swap out the half empty with fresh ones, and then come back with two half-empty sets and have to remember to keep them organized while in storage.
What I'm getting at is that the EOS forces you into 'quantum storage,' where you are working with 3 sets of batteries at a time.
The beauty of the LD01 is it's versatility. Since it only uses 1 battery at a time, I just start a trip with whatever juice is left in the current AAA cell. When I'm done with the trip, I only have 1 battery that is not at full capacity, and that is the battery in the flashlight. This has really simplified my storage and planning of battery use.
It also means that for a shorter trip, or when the nights are short, I can bring just the LD01 and two batteries. For the EOS, assuming you always bring a backup set of batteries, especially if you start with partially used batteries, this means bringing the EOS and 6 batteries. With Li batteries, that's a difference in weight of 3 oz!
The downside of course is that you have to replace the battery 3 times as often.
Also keep in mind, though, that the LD01 can put out a full 30 lumens MORE than even the new EOSR. That's a substantial difference, and when I tested my old EOS and my LD01, the LD01 was substantially brighter.
I will admit, though, that carrying a AA GPS is a good reason to get the LD10. That's why I'm so disappointed there are no high-sensitivity AAA GPSs out there!