Congrats @tantratron!
Very nice to see this productive feedback, so we can all recover from those to-desolder-or-not episodes in this thread!
Indeed, I've also had some luck in the past with failing chips by stretching the limits, but you're often on your own and there is sometimes more luck to it than reason, depending on the failure mode which one mostly ignores. And half of the time you end up toasting it without luck. The usual things are trying to raise power levels, pulling up or down input and output levels, multiple one-shot reads pulling out the data, etc.
An interesting experience I recall from the past, which might help someone: one day I've recovered EEPROM data by reading every byte thousands of times. Data seemed purely random. But it wasn't, as I saw more "bit stability" when raising levels. Because I couldn't raise levels anymore without running the risk of blowing up the device, I took averages of every individual bit and put it to a definite "0" when its occurrence was over a certain frequency, statistically speaking. And then suddenly ta-da, the original data was back! It was a sort of quantum qubit-readout, lol! I had spent more than a week attempting to read it, but it was worth the time in gold as the cost of the data loss would have been so many times higher.
I'm sure this type of failure will reoccur with this particular EEPROM and thanks to your feedback someone will likely be able to get back cal data in the future using the same method.
Hint: if you post your dump, I can always check how far the actual values make sense. Because of the sloppy checksums used, there is a 1/65535 chance the checksum is valid by accident. Very unlikely, but I can verify if you want.