I feel your pain, Mousy..But if it's an emergency, you're inclined to do so and you have access to another X99 mobo (maybe one of the 10 systems you built for your university), you can take the BIOS chip from your X99 and put it in another X99 to flash it.
Boot the functioning X99 into Windows, grab the BIOS flash tool .zip and extract it..Carefully swap out the BIOS chip with yours while the machine is running and in Windows..Run the update.bat to flash it per the Windows Installation instructions (in the Notes) on your
BIOS download page..After the flash and the machine shuts down, swap BIOS chips back again.
Swapping out the BIOS chips may be (probably) easier than swapping out CPUs..Otherwise, wait for EVGA to reply about sending you a new replacemrnt BIOS chip.
Just another thought here..Good luck.
On a side note, I wish that not only EVGA (hint), but all enthusiast mobo manufacturers these days would get onboard with something like
ASUS USB BIOS Flashback where you only need power to the mobo to flash the BIOS..No CPU, no RAM, no nothing needs to be installed to flash the BIOS from a USB stick.