Let's start from checking few things:
- does programmer pass hardware test? please share screenshot from it
- are you using stock USB 2.0 HS cable directly plugged to USB port (without dock station, hubs etc.) ?
- how about when you load random data to buffer (CTRL + R) and write it to 93c66 and next make 10x read - is CRC changing each time?
- could you send me photo how you put eeprom in zif socket?
PS. swap byte is for 16-bit devices (most 93xx) where you can have MSB first or LSB first, e.g. 0xABCD -> swap byte -> 0xCDAB