OK, you've got a battery shell, now think "DC-to-DC" voltage regulator. Such as this . . .
" Step Down Module
LM2596. Input voltage:4V-40V. Voltage regulation: 2.5% - Output voltage:1.3V-35V. "
https://www.google.com/search?q=++dc+volktage+regulator&sourceid=ie7&rls=com...lz=&gws_rd=ssl
Encapsulate the VR circuit in the shell and feed it with one 9VDC battery (or more in parallel for extended AH capacity?) or an auto battery, D, C, AA or AAA battery pack clipped to your neck strap or in your pocket. And there's your extended capacity power source depending on the nature of your use. Feed with a wall socket, 9 VDC AC-to-DC brick for tethered studio use. With an in-line polarized plug you could attach power sources as desired. You'll need to provide a tiny wire port to feed the shell but that can be WR sealed in many ways as desired.
See the external power accessory for the Q body for example.
I haven't done this for a K-body (yet!) but I've used the modules for other similar device feeds (GPS, solar battery chargers, etc.) and output regulation is adequately stable for the purpose.
Got an old defunct cell phone that still charges its battery? Re-use it as an aux power supply with a little fiddling to provide a power out lead. (I'm still trying to think of some really neat use for that that "kernel-of-corn" sized vibrator motor from a cell phone . . . besides a 'whoopee' cushion?.)