You would need to make the Peltier part of the box's wall somehow (with radiators attached to each side?), and then reverse the current flow in summer so the inside is cooled rather than warmed. The Peltier I am playing with is tiny (maybe a square inch) - not sure if they come in more usable sizes.
What would happen if I would put a 5.1V Zener diode across VDDM and GND on the SunControl board? My load is pulling 500mW so a single 1N4733A should do. My hope is that this would reign in the runaway output voltage on the Suncontrol, and also help to stabilize the I2C bus voltage.
The zener will dramatically increase the current on the output. You can put a current limiting resistor inline, but that will change the voltage. I'm charging a battery right now to do the test on the board you returned and another board.
Update: replacing the 6.2V Zener over the solar panels with a 5.6V Zener resolved that issue. Just make sure that the Zener has a useful heatsink attached. Beyond that it will require active solar panel management (ie selectively switching them on and off , for example via the QPM) to control the "Full sun/Full battery" situation.