Using 800us out of 1ms for date processing is alot, especially when you talk about multiple (RTOS?) tasks. If the additional delay is of no/little concern, I would increase the buffer sizes by a factor of at least 10 or so to average out short overloads. In addition, a buffer queue could be useful which decouples the producer (irq) from the consumer (data processing). With circular DMA this can be done using another DMA copying the just recorded buffer to a safe place in a ring buffer queue. Double buffering DMA would be better, but is not avail on your chip.
To observe buffer over/underruns, you can mark the first word(s) in the DMA buffer with some magic values (e.g. extrema) and later check if they were overwritten by DMA hardware.
Finally: is it really neccessary to process each and every audio sample for noise detection? Think of linear DMA wich is triggered by some timer every 1,2ms buying you more headroom for processing+aux. tasks or by skipping a buffer every now and then when you detected an overflow.
