Success! I was able to get access to the BIOS and the device is working perfectly as a happy little pfSense router now 
I used GitHub - nofeletru/UsbAsp-flash: Program allow you to program flash memory on the protocols spi, I2C, MicroWire. Supports CH341a, CH347, UsbAsp, AVRISP(LUFA), Arduino, FT232H. along with the previously mentioned USB programmer. I had to purchase an extra socket that would fit the chip (I opted for the larger of these two Amazon.com)
I connected the 1.8V converter to the programmer USB, then the 200mm socket to the 1.8V converter, booted up AsProgrammer, and followed the steps here (AsProgrammer and other Windows utilities for CH341A · One Transistor) to scan for the winbond chip. I made sure to save a copy of the scanned firmware, just in case, and then on the dropdown next to “Write IC” I selected the “Unprotect → Erase → Program → Verify” option. This worked after a few minutes without any issues!
Anyone can feel free to reach out to me if they need assistance with this in the future, but I hope this breakdown helps! I had to do a lot of digging myself, so hopefully this saves someone some time and headache.