I completely agree that one-per-part singing really brings out the beauty in 16th century choral music. I sing in a choir that specializes in music of this period, and while our live performances usually use two singers per part to fill a room, our recordings are more often one-per-part with relatively close micing.
We do record in churches because we like the reverb, so it's not quite the dry studio sound you're describing, but we do prioritize a clear sound stage where all of the parts can be clearly heard.
We've found that a Blumlein mic configuration (two figure-8 pattern microphones placed at a 90 degree angle from each other) helps to create this clarity of texture, where all the parts can be heard individually across the stereo image, especially when listening with headphones. I can't take credit for this idea though: we learned it from the sound engineer who records the Tallis Scholars, who told us that they record in this configuration.
Here are a couple examples of tracks recorded using this style:
https://www.youtube.com/watch?v=IZgo2Z17nNQ
https://www.youtube.com/watch?v=6r0iyq7AvaU
We do record in churches because we like the reverb, so it's not quite the dry studio sound you're describing, but we do prioritize a clear sound stage where all of the parts can be clearly heard.
We've found that a Blumlein mic configuration (two figure-8 pattern microphones placed at a 90 degree angle from each other) helps to create this clarity of texture, where all the parts can be heard individually across the stereo image, especially when listening with headphones. I can't take credit for this idea though: we learned it from the sound engineer who records the Tallis Scholars, who told us that they record in this configuration.
Here are a couple examples of tracks recorded using this style:
https://www.youtube.com/watch?v=IZgo2Z17nNQ
https://www.youtube.com/watch?v=6r0iyq7AvaU