I'm just wondering if you'll be using millis() or micros() while interrupts are off?
There are fast read ADC chips you could add and 328P's have a fast read 8 bit ADC mode.
Most code runs at clock MIPs but I/O takes a bit longer.
I have timing code that does a digital read, counter increment, and counter timeout check all in just under 1 usec per while loop with zero interrupts since I'm using micros() for time as well.
Change that to an analog read and I'm 105 usec per loop.
IIRC whole sections of the MCU shut down during ADC so as to not affect the conversion, or is that a non-default option?
You should be playing with sound chips at those speeds anyway. 8k samples per ain't much to those, even at higher resolution.