the headers would have to be offset.
Not if you use surface mount headers and socket strips, that way you can intercept the signals on one side, process them and route back to the other side.
You can never get the same versatility as the original chip though, eg pullup resistors and analog IO.
I would not use MOSFETs, not that there's anything wrong with them it's just that you'd need so many. The proper level-shifting chips would be easier I think.
Rob