If there are only seven EEPROMs it seems there is one missing from the board. (7x 512KB = 3,670,016, I should have realised that earlier)
The unusual ROM size might be the reason it didn't boot in emulators before. Most emulators will try to detect the mapper type by the ROM size and internal header. I wonder if it would still boot if you used 512KB of null data instead of that 8th segment? Maybe not.
Maybe there is something different about that eighth segment in the final release and the one the your board expects. If data were slightly offset within that bank it could explain why it would crash. I think the game executes code often from the final 512KB and regularly jumps between that area and the beginning of ROM, so that segment might be crucially important. If there are even small changes to code within the missing bank it could affect the other banks greatly as well.
If it is just a small code change, then perhaps it could be circumvented by swapping the first 512KB with a good ROM as well? It might be worth a try.
I can't really think of much else to do. Some deeper probing would be required for definitive answers, unless other people have some ideas.
Even if the ROM won't work it should still be possible to examine the data for interesting changes. It could be interesting to see how similar each segment is to the corresponding segment in the final release. That would be a good way to notice changes without having to play the game.