If you want to use lots of different board types without re-routing each single board and aren't put off by the price of four DIP-TO-IDC sockets, you could do this instead of cutting paths & soldering on the circuit board: use a not-too-long ribbon cable to connect two 40-pin DIP-TO-IDC sockets together. (I believe that DIP-TO-IDC sockets don't exist in 32-pin form) Then saw through one of them and use tape to make it a 32-pin socket, which will plug into the socketed cart. Solder a cheap 32-pin socket to the used pins in the socket at the other end (that is, turn pins against pins if) which you will plug your EEPROM chip into. Now you can cut up the parts of the ribbon cable in the middle of it and re-route the lines that way. Do the same for the other one, and you have a PRG and CHR ROM-to-EPROM converter. It might be more work than doing it on the circuit board in a way. But I've found that it's freaking hard to solder wires to thin circuit paths on the board, so I would prefer doing it this way.
OT: For my EPROM emulator, I have a ribbon cable going from the emulator into a socketed board and a socketed ribbon-cable with an SRAM chip attached to it to emulate CHR-RAM. A wire then goes from CHR /WE inside the NES and is attached to a loose wire on the SRAM chip. My EPROM uploading program then first writes the CHR-ROM data to the EPROM emulator along with some code to copy it to CHR-ROM that will do the proper bankswitching depending on the mapper type. After it's done copying, the uploading program copies the actual PRG-ROM to the EPROM emulator and resets the NES again.
This method lets me run almost all games made with just a TKROM, SKROM, AOROM and a UNROM-board by simply changing to the appropriate board. The only game that doesn't work is Noah's ark, which I think does some nasty writes to the CHR-ROM which would be ignored on the actual cartridge. It's probably the best way to play games on the real deal until someone among us manages to make an FPGA-based universal cartridge. :)