Hi Amwidkle,
what follows is how I understood it. If I'm wrong, I hope some mod is reading and will correct me.

To begin with:
"What I would really like to have is an NMR policy that does nothing if a country NMR's once, but if a country NMR's twice in a row over two consecutive phases"
Well... this is what happens when you set turns=0 (Feature is "off").

So with this in mind, the number of turns you set is how long the "CD after only one NMR" will work. Btw, a turn is the group of phases (from 1 to 3, depending on *if* there are retreats and builds after diplomacy) with the same time-name, so it's usually a season. After that number of turns, feature will be turned off.
IE, in a Classic:
Turns=1 - you go CD if you miss even only one phase in Spring 1901; from Autumn 1901 on, you go CD only if you miss 2 consecutive phases.
Turns=2 - you go CD if you miss even only one phase in 1901; from Spring 1902 on, you go CD only if you miss 2 consecutive phases.
Turns=3 - you go CD if you miss even only one phase in 1901 or in Spring 1902; from Autumn 1902 on, you go CD only if you miss 2 consecutive phases.
...

What happens now if the feature is on and NMRing players are sent in CD?
Active players' orders get unreadied (switched to "saved"), the game doesn't progress and the last phase restarts. But this means that if all active players "finalize", then the game will progress, no delays, no matter if a replacement was found or not, because the CDed player is not an active player.
Well, the delay number is just how many times that single phase will be repeated because of NMRing players. After that number of times, the phase will progress anyway, whether there are NMRs or not.

And yes, when you go CD your current result for that game is "Left" and it will appear both in the results' list of the game itself and in your personal stats.


If I may suggest you a thing, this would be certainly to keep in mind that the result you got from the Feature can substantially change depending on what are the other parameters in the game, so there's not a "perfect" NMR-setting that's good for every game.
IE, you could expect a big difference in how a NMR ∞/∞ would work in:
1 - a passworded 7-10 players game in which only well-known reliable players were invited;
2 - an open game on a large map without RR requirements.
In the first case you wouldn't even notice the Feature is on, unless a player has some serious sudden issue and disappears without even ask for sitters/pause/extend.
In the second, you would very likely have in it any sort of unreliable players, quitters, sore losers, newcomers losing interest in the site after a few days, etc... and so... oh! you'll notice the Feature is on! If you're unlucky enough, your game could soon become a nightmare of delays.
So my advice for you when you join/create games is to not focus only on NMR setting, but to check also the other parameters, especially RR requirements and number of players.

Lastly. While I search for games to join, I notice this feature is often misused. If it was used properly, it'd be a great help to have enjoyable games.
I believe there are many players like you having doubts about it, but unfortunately explanations are not cristal-clear and many players just prefer to turn it off than to learn to use it.
Happy to hear there's someone bothering to ask, instead.

Hope this helped you. :)