It looks like I could use SPI to burn the bootloader as well according to this page: https://docs.arduino.cc/built-in-examples/arduino-isp/ArduinoISP/#:~:text=of%20the%20target.-,How%20to%20wire%20your%20boards,-The%20following%20table.
I'm not familiar with SPI but I assume that this would circumvent the issue with using serial communication? With the caveat that I'd need another (functional) board like you said?