Your idea solar GameBoy looks great too.

It seems Embox fit for your purposes as an operating system which allows running a lot of ready to use Linux software and at the same time save hardware resources.

Embox in the one side can run complicated Linux applications Qt (, PJSIP (, or OpenCV ( and the other side doesn't use excessive resources. EFM32 for example. Except this, Embox run on Dialog board with BLE, USB, HTTPD, TELNETD, and have < 50 uA current consumption of course if you are not using the applications