I have a Farallon Ethernet card installed in my LC III, and I am considering this mod as well.
The gap between the top of the Motorola and the side of the NIC facing the CPU is about 1/2".
To account for fit with other Ethernet cards, ensure adequate airflow around the heatsink, account for the thickness of the thermal pad, and a healthy margin of error, you should subtract 1/8". Now you're left with a
recommended maximum heatsink height (not necessarily absolute max height) of around 3/8" , or
~9.5mm.
The CPU surface measures approximately 7/8" or
~22mm.
For a maximum heatsink size of 22 x 22 x 9.5 mm, I think the one below is as good as close as you're going to get.
Easycargo heatsink (
20mm x 20mm x 10mm, 10 pcs @ $7.99):
https://www.amazon.com/dp/B07BDKN3XV/
This heatsink will cover 90% of the surface of the CPU. You can attach this heatsink to the CPU, FPU, and the VLSA controller (this one is larger than the other two), and still have parts left over to cover a lot more LC III's if you only do the CPU. That ain't bad for something that costs just $8 and maybe an hour of your time.