The EPROM idea is interesting, I have explored it but I don't think it could work. The main issue is that the 8Kbyte RAM chip which holds the calibration data (TC5564APL-15) is also used to store the processor stack, firmware variables, user's memorized measurements etc.
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From the schematic, we know the RAM is used as follows : - Calibration RAM data is from 0040 hex to 01FF hex with a special hardware mechanism to prevent accidental overwrite of this area. - General storage RAM (processor stack, miscellaneous variables, user measurement FIFO etc) from 0200 to 1FFF.
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?.... In summary, replacing the RAM chip with an EPROM would not work. One (strong) reason is that the processor stack and RAM storage would not be writable.