Is the interface to the EPROM chip a serial interface or a parallel interface?
With a serial interface, it should be quite easy to get something working, since it probably conforms to one of the already existing serial protocols. There are lots of references for Arduinos and serial interfaces, and it should be easy to convert. Plus you would still have enough pins to run a LCD to print out the values.
If the interface is a parallel interface, it might be more difficult.
Either way, you will probably need the manual for the EPROM chip to understand how to interface with it.
We have a Stratasys SST1200ES that uses cartridges too. They have a One-Wire chip that holds the info, and it can be read serially from the two pads on the cartridge. The problem is that the data is encrypted.
There is a 1-Wire library for the Arduino, and I have used that to read the chip contents.