You have to program these new eproms with the data from the old ones. The old ones are 4 bits each and the new one is 16 bits.
This means you have to combine the 3 x 4 bits to 12 bits and then extend to 16 bits.
So the first action is to read the 6 proms from your board and then combine the nibbles from the 3 that belong together. The order of combining depends on how you connect the data lines on your new board.
Lets say you connect D0-D3 to 6E and D4-D7 to 6F and D8-D11 to 7F and leave D12-D15 unconnected, you have to take the first nibble of 6E and put it in the lowest nibble of the 16 bits data. Then the first nibble of 6F and put that in the second lowest, and the one from 7F goes in the third lowest. The last nibble is set to 0xF (All ones).
So the data looks like 0xFZYX, where Z is data from chip 7F, Y from 6F and X from 6E.
Edit1: yes you could use a hex editor, or if you know a bit of programming write a simple bit of code to do it for you
Edit2: Looking back I should have used "leave the not used data lines unconnected"
