My first and foremost suggestion would be that you invest in an SPI programmer and a SOIC16 chip clip. It will be by far the fastest and easiest method to flash the switch, if you value you time at any value above $0.
This is completely untested, but if you already have a serial console, you could transfer my firmware build over zmodem or something and then flash it. This will take forever over UART and will likely not work anyway, because the mtd layout is completely different between Leo's firmware and the SPI firmware I have created.
You're more than welcome to try alternative methods to install the firmware, but for the moment I can only support SPI flashing using an external programmer.
Installation doc is at the bottom of this post: https://watchmysys.com/blog/2020/06/ms220-8p-custom-firmware-from-scratch/