if you have the lifepo4 in parallel with your nicad. at full charge the nicad will be 141V and in order to match that with lifepo4 you would have about 40 lifepo4 cells in series at 3.5V, just kinda an arbitrary example.
the nicad will be full expended when they get to 100V and there is risk that even that voltage cutoff would allow some cells to be pulled under 1V which is not healthy for them and i assume the saft 5S modules supervise that.
your 40S lifepo4 will go as low as 85V, though 100V is a reasonable cutoff number and you could actually get most (90%)of the capacity from the cells at 100V low shutoff.
the schottky diode is there to protect the good side from discharging into the bad side if the voltage on the bad side drops so low that it would cause the good side to overdischarge and pull the cells below their minimum operating voltage. that could damage cells in the good pack if they are in parallel so the schottky is there to prevent the current from flowing into the pack from the other one. it always allows the current to flow out, just prevents current from flowing into the pack if it is dead and therefore protects the good pack from overdischarge.
that's why i asked if you could use another pack in series, because then it is easier to use the pack without the need for a diode in series. the diodes get hot too, and for a 200A draw, really hot. then maybe a FET type isolator like tiberius is making would be more appropriate in any case since it doesn't soak up the power and make heat as easily.
the used nicads in the saft 5S packs should be in relatively good shape if they are supervised, even after many years but finding them used, or even finding a junkyard which haas a used vehicle is unlikely without some real effort i would assume, but then your charger would be working at the same level and just charging more cells if they are all in parallel, but again you have to worry about putting packs in parallel even if they are the same chemistry and worry if the charger would see endpoint too, but this seems like a more reasonable effort. it would extend your range and give you a little more acceleration maybe, but you would not get the increased top speed you may be able to get by adding the lifepo4 or whatever in series. but that speed boost may be limited in the controller anyway.
others are much more knowledgable about batteries than me though so maybe they can offer an opinion.