Peltier Fridge Heat Loss
Welcome to Peltiers. They are convenient and small, not efficient. They are beaten hands down by any compression cycle cooler.

If your Peltier is cycling on and off to maintain your target temperature, then there's some very low hanging fruit to harvest. Heat pumped is proportional to I. Heat generated is proportional to I2. This means they run much more efficiently at 100% duty cycle of just the current they need to maintain the temperature. This also prolongs their mechanical life, less expansion and contraction breaking the bonds as their internal temperature cycles. You would ideally implement a PID driving a filtered buck converter to feed the Peltier.

One of the Peltier manufacturer's websites has an online calculator. Given required heat flux and temperature differential, it will give you two solutions for their hardware. One is the smallest solution, the other is the lowest power solution. The first is run near their maximum rated current. The second is typically two or three times as big, and run at a third of max rated current (remember that I vs I2 ratio?). Higher initial cost, but much lower running costs. Here's a handy tutorial on the issues.

I would use an alli block, just the size of the Peltier, on either side, before transitioning to a larger heatsink, to allow more insulation thickness than just the Peltier thickness immediately around it. There is of course a tradeoff between conduction path length and insulation thickness. 

Every extra degree the hotside runs hotter needs more current, and therefore more waste power dumped into it. Make that hotside sink as large and as low C/W as you can. Maybe even evaporatively cool it.

For the lowest power consumption, you might want to make ice in a freezer, and use that to cool your insulated box, replenishing it every 24 hours, perhaps with a fan or pump to maintain the temperature.