I think you might be overthinking things if you haven’t tried just using a stand to get more airflow. Tom from XMG ran a test between using a stand and not on their new Alder Lake thin and light and had a 10C max temperature difference and a +44% performance gain under a sustained load.
Last time I looked most cooler pads blow up (all the one on Amazon I checked like the Targus Chill Mat, the Cooler Master NotePal, the TopMate, Havit and one Liens all seemed to).
As for a chassis mod, it looks like it’s $100 for a Bottom Cover Kit if you want to buy one and have at it, although opening up the grill too much may actually reduce airflow efficiency.
The fan tables and fan control are in the Embedded Controller, not the BIOS, which is open sourced and on Linux, there’s an easy to use fan control tool and also a straightforward way to set your desired fan curves.