The original project can be found here. The modified .ino is attached below. Added support to change Vcc from 5V to 6.25V during the programming, using voltage boost converter (MT3608). The original schematics is followed most of the time. There is an error in this schematics which does not match the arduino code: D12 controls A9 and D11 controls /OE but should be vice versa. In the final implementation D12 controls /OE (0, 5, or 12V) and D11 is used as Vcc control pin to set the boost converter to 5V or 6.3V. Instead of BC307, BC560 was used.

The first working version looked like this:

The other option is: https://github.com/AllanGallop/Arduino-Eprom-Programmer