What would a more powerful processor be?
http://www.logicsupply.com/products/artigo_a1000 
I actually don't know. Someone else will have to guide you on something between an Arduino and a Pentium.
The reason I had the 3 arduinos serially laid out is so that each could do one specific job, and that job only.
I understand. But first you need to determine if it's even necessary to have more than one Arduino involved.
stereo
One Arduino per channel with the kill button wired to both.
Coding Badly: Hmm. So I believe it would have to be 28000 Hz, 16 bit stereo, as that is the maximum our main 7 second box runs, and there's no point in running a massive quality stream out just to be re-compressed for radio again.
That means an external ADC and an external DAC (per channel).
(((28000*2))*16)/8 = 112,000 bytes per second (per channel)
* 7 seconds = 784,000 bytes of storage (per channel)
16000000 / 112000 = ~142 machine instructions per sample (per channel)
A run-down of what needs to be done...
- Get a new sample from the ADC
- Record the new sample to a circular buffer
- Read an old sample from the other side of the circular buffer
- Send the old sample to the DAC
- Check for a button press
I suspect that can be done in 142 machine instructions but you will very likely have to avoid the Arduino API (instead of digitalRead, read the PIN register; instead of using the SPI library, access the SPI registers directly). You will probably have to turn off the millis interrupt and setup a timer to provide synchronization.