I have spent most of the day trying to make the C library faster and unfortunately due to the way the SPI driver works in Linux it does not look like it will be possible to get the full speed out of the ADC.
The screenshot from my logic analyser below shows the problem. The linux SPI driver sets the enable line low early and waits more than the length of an extra byte before setting it high so you loose the equivalent time of two bytes of data on each sample. This seems to be a feature of the SPI driver and I can not find a way around the problem. Once the enable line does go high it takes approximately 22us for the library to process the data before starting the next loop. I have tried trimming the code down to the bare minimum but I couldn't get the time much below 22us so I think this is the limit of the C library and the Raspberry Pi.
The pigpio library gets around this problem by bit-banging the SPI bus instead of using the SPI driver which may allow a faster sample rate but as this could make the C library incompatible with existing code as well as other hardware platforms I don't want to make the change to use pigpio on our C library.
You could try using the pigpio library and example code for the MCP3202 in your project and see if it gives you any better results.
Another alternative would be to connect the ADC-DAC Pi to a separate microcontroller like an Arduino. The Arduino could read the samples from the ADC and send the data to the Raspberry Pi via the I2C or UART port. The main advantage this is the low level of hardware access would give you consistent timing for the sample reads. The Arduino would also only have a single task running on the microcontroller where as the Raspberry Pi has dozens of other processes taking up CPU time.
With an Arduino Uno or any other 5V Arduino you could run the ADC-DAC Pi at 5V allowing you to use a faster clock speed on the SPI bus. A 5V Arduino would need to use a level shifter for the connection between the Arduino and the Raspberry Pi to drop the 5V bus down to 3.3V.