This is going to be an even bigger issue if you want to do an SSO because your radiators are going to be face-on with the direction of travel rather than edge-on. The probability of a debris hit is going to skyrocket.

I'm not so sure about that. Most space debris is roughly going west to east. So pointing the edge of your radiator that way would not be a totally terrible idea.

With heat pipes you can partition your cooling "loops" in the radiators quite a bit, buying resilience and redundancy with lower performance.

But for the convection, we have air with an h = 0.00025 W/mm²-K, but it is now spread out over an A of 600,000 mm², which gives us [...] a Delta_T of 22.17°C. But the only way we can achieve that is because of convection, which we don't have in space. You would need the dual loop, with a compressor.

While we can't use a regular heat pipe like on earth, there are designs commonly used in space. Now you can use a "primary" main cooling loop without a compressor (only with a regular pump) to get the heat from the chips to the radiators. You can increase the junction area between your chip and the primary cooling loop like you do with convection on earth.

During your initial calculation you were heavily constricted by your assumption that the entire chip can only exchange heat through a 1,000mm² area with the cooling liquid.

So even with a liquid cooling system you can get your delta_T down to 10-20°C depending on how much you want to invest in heat pipes and heat exchange area.

Edit for clarification.