The trail camera uses two parallel banks of four series AA cells to get enough oomph for its IR floodlight. I’m not convinced using bucked lithium AA cells in that configuration is a Good Idea, but it’s worth investigating.
These are labeled HW, rather than Fuvaly, because it seems one cannot swim twice in the same river:
In any event, they come close to their claimed 2.8 W·hr capacity:
The lower pair of traces (red & black) are single cells at 2.7-ish W·hr, the blue trace is a pair at 5.4 W·hr, and the green trace is a quartet at 9.8 W·hr. Surprisingly close, given some previous results in this field.
Recharging the cells after those tests shows they all take 3 hours ± a few minutes to soak up 730 mA·hr ± a few mA·hr, so they’re decently matched.
Measuring the terminal voltage with a 10 mA load after that charge lets me match a pair of quartets to 1 mV, which is obviously absurd:
The numbers in the upper left corner show the initial charge of four cells at a time required the same time within a minute and the same energy within 4%.
Sticking them in the trail camera must await using up the current set of alkaline AA cells.
Bonus: a lithium fire in a trail camera won’t burn down the house.
After all, pictures like this are definitely worth the hassle:
Looks like a pair of WiFi antennas …
The Smell of Molten Projects in the Morning 
My (Google-based) understanding of the problem with similar cells is that they rapidly deteriorate with successive recharge cycles?
And the winner is… A rechargeable lead-acid battery. A Burrel Edge HD + 3G has been in service three years, 3900 picuters taken. Still shows P5, ie full charge. Temperatures been +30C downto -30C. Wrapped the battery into several plastic bags and then fitted into an (empty ;-) ice cream box.
The camera has a coaxial jack labeled 6 V / 2 A and I knew I saved a foam box for some good reason!
Thanks for the suggestion …
In theory, the lithium cell shouldn’t deteriorate faster than usual, but who knows what corners they cut to stuff the charger in there along with everything else.