The backup plan was to use IR sensors with an ON or OFF digital output only like these.
It says:-
IR sensor tuned to 38KHz, perfect for receiving commands from a TV remote control.
True, but useless for what you want. This is because the LEDs need modulation and the sensors only pick up pulses if you send less than 30 or so pulses without a gap.
Is multiplexing the best idea then,
It is one idea. Each sensor needs it's own input so imagine using an 8 input multiplexer then you need 300 / 8 = 38 chips. Each one of these has one output that feeds into the next level of multiplexers so that means you need 38 / 8 = 5 chips on the second level. Each one of those 5 can feed into the on chip A/D multiplexer so you will need 38 + 5 = 43 chips. Doable but not very economic.
As has been pointed out you need to scan those at quite a rate. The thing is that most of the time the sensors will be detecting nothing.
If you used a port expander like the MPC23S17 this has a capability of 16 bits. Each of these bits can cause an output ( called an interrupt output but don't uses it as an interrupt ) to change when any of these bits change. Therefore you only have to look at one bit to in effect scan all 16 bits for a change. This greatly speeds up the process of scanning all the sensors. Only when the interrupt bit has changed do you need to go into the port expander and find out what particular sensors have changed.
You can use 8 of these MPC23S17 on the SPI bus simply giving you 128 sensors. However, it is not too difficult to cascade three banks of these to give you the 300 you want. So that is only 19 chips you are using.