Hi plato_3,
First of all, can I ask the most obvious question: why not just use an Arduino Mega? 16 analog and 54 digital outputs...
Second question: do you actually need those analog multiplexers at all? Might be worth experimenting to see if you can loose them completely. Just connect a diode up to each sensor, common the diode outputs and connect that to your analog input. Since you will only apply 5V to one of the sensors at a time, that's the sensor you will be reading. The diodes will prevent the voltage leaking away to ground via the other sensors.
As for your shift registers, you can use shiftOut(). If you have 3 registers, send 3 bytes out with 3 calls to shiftOut() before pulsing the latch line.
Paul