Hi guys, thanks for your suggestions, I'll check them out now. There's just been a slight change of plan regarding the IR sensors. I was suggested some more suitable ones by a user on here called Chagrin, who also very kindly explained how they would work. The sensors are Vishay TSSP4P38. They give out a PWM digital signal that spends longer on each cycle at 0 V than 5 V the closer that the object is using a separate IR LED to reflect off the object. I would then use pulseIn() to sample and convert the PWM to a suitable value. This seems really good for my situation - long wires carrying analogue signals would have problems with noise etc. so I think these are a nice solution.
Using these new sensors would necessitate the use of digital multiplexing now, right? I guess that means your two-tier multiplexing solution is the best! 288 / 16 channels = 18 multiplexed lines. Then using two more multiplexors I need less than 10 or so pins on the board which is okay. I'll do the exact calculations when I decide if I'm using 8/16/32 channel MUXs.
What are your feelings on this solution with the new sensors?