My primary concern in a project like this is to not lose the original EEPROM contents. Nothing else matters! In the end, I won't be any worse off than I am before I start.
The next problem is how to extract the SPI data. There are a lot of microcontrollers that can handle SPI. Almost all of them, in fact. But what to do with the data I read? I might want to put it somewhere while I figure out what to change. Maybe I want to print it. It could be that I already know which bytes to change. In that case, I would just read a byte, substitute if necessary and write a byte. There would be no need for storage, just two chips on a breadboard with something driving the SPI bus.
But we don't know! Nothing was said about how the changes would be implemented.
Since I can easily read SPI on a Raspberry PI and it already has a file system for saving the contents, sure, I'm going to do it that way. It helps that I have a couple of PIs sitting here. The alternative might be an Arduino because there is already an SPI library. But storage is something that needs to be built, it isn't included in the box. More work... Using raw hardware (like a PIC) is just too much effort. First I have to get SPI working, then I have to read the data and then what? I guess I could use a Basic Stamp and bit-bang the SPI but that seems like a lot of work.
No, I'll take the high level approach and use a board with a file system. I just know I'm going to want to print the file...