Lol, eneloops. Ni-Mh have tremendous self-discharge they probably will be dead in a week just lying on the table. Use alcaline batteries, dude. They don't self-discharge and have a combined capacity much larger than even a Li-Po battery.
I'm not sure if you are being serious.
I am dead serious.
https://en.wikipedia.org/wiki/Self-discharge ... Li-ion absorb the least amount of self-discharge (around 2% to 3% discharge per month) than lead-acid at 4% to 6%, while nickel-based batteries are more seriously affected by the phenomenon (NiCad, 15% to 20%; NiMH, 30%). Primary batteries, which aren't designed for recharging between manufacturing and use, have much lower self-discharge rates, with shelf lives of 2 to 3 years for zinc–carbon batteries, 5 years for alkaline
You're trying to use high-current high self-discharge Ni-Mh accumulators in a device that needs super-small current and low self-discharge batteries, such as alkaline.
Speaking about capacity, AA batteries have a capacity over 2,500 mAh that effectively makes 2xAA a replacement for 2500 mAh 3V Li-Po battery, while Ni-Mh have real measured capacities in a range of 1200 to 1900 mAh.
Use those eneloopes for the camera, for the keyboard you should use good alcalines like Duracell Turbo Max. My Filco with the same chip (BCM27030) lives on those for more than an year (with 6 months official battery life). I assume HHKB BT, declared 3 months, would work for 6+ months on turbomax alcalines. I personally use it since it came out, for more than a month already.
There are even better, Lithium AA like GP Lithium but they're pretty pricey.