As an engineer "forget the datasheet" is not part of my way of working. It is not a general guide , it's the bible.
As a PhD physics researcher working on some the world's largest experiments, I take datasheets with a grain of salt. They are a clue but you must evaluate devices in the mode you use them. Often devices change but not the datasheets.
I get the impression you are confusing a statistical measurement , ENOB, with the spec for the accuracy on one ADC conversion. The two results are compatible and not contradictory. They are different things.
Accuracy of one conversion is a statistical measurement. Accuracy is always a statistical measurement.
Did you read the Oskar Leuthold paper on the AVR ADC? He is an engineer working for GEC Plessey Semiconductors. He designs fast, 200 Megasample per second A/D converters.
What is wrong with his testing of the AVR ADC?
I am logging physical quantities, not audio.
Audio is a physical signal. Some of the most advanced research in high quality ADCs involves audio.
Are you able to comment on whether sleeping the CPU would break the SPI streaming or is the protocol robust enough to stand a circa 100us hiatus?
Using ADC Noise Reduction Mode is likely to cause problems with an SD transfer. Atmel documents suggest that Idle Mode could work O.K. The SPI controller is stopped in ADC Noise Reduction Mode and that could cause a glitch.
That's a comment not a proven fact. My original library allowed interruption of block transfers but I kept having problems so I removed the code.
If you need accuracy at 50 Hz why not us an external ADC? I use external sigma-delta ADCs frequently. I wrote a fast Software SPI library that runs at about 2MHz to access external ADCs since it is difficult/impossible to share the hardware SPI bus with the SD.
At 50 Hz you could even use low cost I2C ADCs. Here is a family of 18-bit delta-sigma ADCs I like a lot (maybe too slow for you). They have a 0.05% on-board voltage reference and an on-board PGA. http://ww1.microchip.com/downloads/en/devicedoc/22088c.pdf
. It could give you 14 bits at 60 sps.
This may not work for your application but there are many choices that are easy to use. Why fight with the AVR ADC if it doesn't meet your requirement.
I mainly play with pushing the AVR ADC as a game. For serious hobby measurements I use external ADCs/sensors.
I am now mostly using Cortex M4 STM32 processors, not Arduino. I run ChibiOS/RT as the OS.
Here is an example board https://www.olimex.com/dev/stm32-h407.html
it has three really fast 12-bit ADCs that can run in parallel.