Peltier based DIY fridge help

I want to build a Peltier-based refrigerator for my student accommodation, where traditional fridges are prohibited.

While I understand that in terms of efficiency peltier modules are shit, I'm still going to do it because I don't really want to mess with a fridge compressor.

I am also aware of the huge energy usage, since I don't pay for electricity I don't care.

I fully acknowledge that this DIY approach will likely be more expensive and complex than purchasing a ready-made mini-fridge.

However, the restrictions in my accommodation make a standard fridge impossible.

I have sufficent cooling for the peltier module, I am using a CPU heatsink with a fan, the cold side goes to sub zero (It forms ice).

I did limited research on the topic, (I watched the Technology Connections video making fun of the shitty peltier mini-fridge), however from my understading, with the correct insulation it should be possible.

However I don't know where to start. Will a standard cooler for camping be enough insulation (I was thinking of just making a hole and putting the peltier module in), also how big can it be before its a problem?

Can I just brute force cooling, I have like 4 peltier modules (2 TEC1-12706 and 2 TEC1-12703).

Can I just shove more current through them?

Does anyone have any advice?

EDIT: This is 40% me wanting a fridge and 60% spite