6SN7s are drop in replacements when you change out the socket. By that I mean resistors need to be changed. And that is the tube that was probably in mind when the FP III tube socket holes were made large enough for octal tubes.
As for using 4 - 76 tubes, that would look cool! I don't know what the FP III power supply can handle. Hopefully Doc or PJ or PB will answer.