I believe a USB WiFi dongle will be a better idea than modifying live images of various distros, and others are already pointing you in the correct way for that, but I feel the need to correct one thing:

Okay, so maybe I can add some driver files to the LiveUSB or something? . . . nope. Not a good idea, because the other part of the whole fix is installing firmware, which has to be in place before the drivers will work -- but this chip is also still being used by the onboard Mac OS.

The WiFi module doesn't have any persistent memory for firmware, which is why the system needs to bring its own firmware - it is uploaded to the chip on every boot as part of driver initialization. So there is no risk of interfering with macOS here.

The installation in the guide refers to putting the firmware in a place where the driver will be able to find it. In other words, you would be installing the firmware on the Linux system, not onto the WiFi module.