I upgraded the WiFi cards in my X200 units by installing Coreboot, which has no PCIe allowlist. https://www.neilvandyke.org/coreboot/ I don't know the state of Coreboot support for X220, and the entire process can be a headache, but it might be an option.

I understand some people instead use modified stock Lenovo BIOS to defeat the PCIe allowlist.