GB-BKi3HA-7100 BIOS recovery — CH341A + MX25L8073F (1.8V chip)
The BIOS chip is a Macronix MX25L8073F. The CH341A detected the chip without issue, but when I added the generic 1.8V adapter, it stopped recognizing it. The solution was to ignore the adapter and connect it directly.
To slightly lower the voltage, I used two USB extenders between the PC and the CH341A. Software: Modified official CH341A version, available at https://www.instructables.com/CH341A-Programmer/ — chip selected manually (SPI 25 Series / Macronix / MX25L8073F), with the NUC completely disconnected and the SOIC8 clip in place.
First, I read and saved a dump as a backup, then I opened the official firmware from the Gigabyte website for the GB-BKi3HA-7100 Rev 1.0 and flashed it using Program. It took about 6 minutes. When finished, I removed the clip, and the NUC booted with an image.
Post-recovery shows an RTC error, but nothing serious. This information is useful to anyone who might find it helpful, because I tried everything and since I had put it up for sale and someone asked about it, I wanted to make one last attempt, haha.