If you have the required tools, this mod should cost you about 10$ of materials (excluding the Korg NTS-1 itself of course).
You'll need to print the replacement side planel using a 3D printer. If you don't have a 3D printer, you can ask a friend who have one or find a fab lab near your home.
With this mod, I usually get about 4h of battery life (I used an old battery, so your mileage might be better). The battery can be charged with a separate micro-USB port, and the battery power can be switched on/off. Just make sure you don't leave battery power on while providing power with the regular micro-USB port at the same time!