I must confess, I don't know the teensy... I can only suggest 3 * 16-bit 1KHz equivalent ADC channels per DUE as long as the sampling frequency remains under 1 Msps.
To communicate between the DUEs, IMO the easiest way is Serial (Serial, Serial1, Serial2, Serial3 and Serial4 (yes, you can have Serial4)). The fastest way to communicate between 2 DUE could be SPI with TurboSpi Library (42 MHz).
Anyway your project is far from standard and would deserve some serious study, particularly for the amount of data to transfer between MCUs and your PC in order to draw a relevant solution.
BTW, a DUE has become an affordable 32-bit Cortex M3 (~ $15)