@caleb In your case the chip is soldered on and I only see four options:
1) Get the flashrom source code, See why it throws that error and optionally jerry rig it to ignore that. (Very much not recommended in a board that still works, but ..)
2) Send the board in to be repaired (which might just mean that they replace the board). Only useful under warranty,
3) Buy a whole new board.
4) Buy a new BIOS EEPROM, disconnect the first from power (not the whole chip, just the power lines to the chip. And use wires so you can reconnect when the board is live. PIggy back the new BIOS and power it it…