This is why I don't solder the addressing jumper directly to the EEPROM, I use an adapter with the address jumper installed so that it can be removed and programmed without issue.
I would suspect that with the pins shorted, you would use offsets of zero since the address jumper sets the read to be at the end of the EEPROM, this may look like a 4 kb EEPROM to the programmer. I haven't verified this myself, just speculation on seeing what the address jumper does.
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