Chiphead,
I am no expert but I was recently told the spider gears and the side gears could be "mixed and matched" but the ring and pinion should be replaced as a pair.
I do not know what a cross shaft is (maybe an axle shaft)? Can you find a cross shaft in this picture of
the torque tube and rear axle ? (taken from Kieth Hardy's fine website that is part of
The Old Car Manual Project. Tim