A Flex PCB connecting the OCP2 connector would allow to put the converter board behind the NIC board, allowing the NIC board to be exposed to the aluminum case to use the case itself as a heatsink (would need a split case so the NIC board can be screwed to one side of the case, pressing the main chip against it via a thermal pad).

As a stop-gap, I'd see if there was any way to get airflow into the case - I'd expect even a tiny fan would do much more than those two large heatsinks stuck onto the case (since the case itself has no thermal connection to the chip heatsink).

My goal was to get a fanless setup (for a quiet office).

If that's not a requirement just get the Raiden Digit Light One, which does have a fan (and otherwise the same network card).

If I could design an adapter PCB myself, I would go straight to OCP 3.0, which allows for a much simpler construction, and TB5 speeds.

Alternatively, there are DELL CX422A rNDC cards (R887V) that appear to have an OCP 2.0 connector but a better heatsink design.