Reading Array of Phototransistors With Raspberry Pi
The problem seems to elaborate to a need for acquiring the digital data generated by the ADC, via a single-line interface. 

There are several ADCs available, which support such single pin serial line interfaces. For instance:


Dallas 1-Wire data interface ADCs, such as the Maxim DS2450
Analog Devices AD7866, which has two independent single-wire serial data outputs - use any one.


Basically, one needs to look for ADCs with such a single data pin interface, rather than the SPI device specified in the question.