I offer a standalone Programmer, that transfers compiled sketches (*.hex file) from SD card into Arduino flash memory, where it then runs from.
It uses a '328P set up like a ProMini to accept the user choice of file, read the SD card, write it to flash, and report on the result.
You could use that code as the starting point and make the necessary changes to read from an EEPROM chip instead.
You'd also have to write the code to receive files and put them into EEPROM for later transfer out.
Also, see Nick Gammon's website about the transfers from SD card