PlatformIO (or rather, the custom third-party platform code) is able to upload a firmware directly via some upload methods: See GitHub - maxgerhardt/pio-nxp-lpc1769-arduino-test: Simple project for testing Arduino support on the NXP LPC1769 chip using a custom platform.. However, if there is a bootloader involved, things might be different. Uploading a firmware this way to the wrong address will override the bootloader, and you really don’t want that. So the safest route would be to let PlatformIO generate the Marlin build and then take the compiled .bin file and let the SD card bootloader handle the rest. If you have no restraint in experimenting with direct uploading (and fixing some upload addresses if they’re wrong), you can try it… You should work on obtaining a full memory dump of the current flash though first, as that will be your only means of recovering.
As you can see in the schematics, the SPI pins are simply duplicated on the SPI header, together with a +5V supply.
The signals are of course 3.3V level so take care of that. Plugging in a premade SD card module like MicroSD card breakout board+ : ID 254 : $7.50 : Adafruit Industries, Unique & fun DIY electronics and kits should work out of the box though (has 5V → 3.3V voltage regulator and level shifters, so it can be used on 3.3V and 5V microcontrollers). Also see pinout diagram.
If none of the traces are physically broken (the connections on the SPI header still go through to the MCU), that should be the easiest method of fixing.