I don’t think you can flip the cable on system 6 sound boards. The voice card side is not a typical ribbon cable header connector.
A good way to rule out the ROMs is to press the diagnostic button on the sound card. If it plays the sounds and voice prompts properly, you can rule out the ROMs. The list of sounds any voice is listed in the FP handbook, I believe.
Playing wrong sounds is usually bad connections between the driver board and sound card which is why header pins and associated connectors are suspect. When you reseated connections, did you the corresponding connections on the driver board?
Do you know if the ROM sockets were replaced on the sound card? Can you try lifting and reinserting the ROM on the sound card?