Of the three choices, the NuVinci has the lowest range, so if that's important to you, it should be the lower on the list. I can't say anything more about them.
I have an Alfine 11 on my Day 6 (the Buick) and it's very nice. It makes no noise at all; you won't get a quieter ride. I think it has an advantage in being more familiar to bike mechanics than the other two, but you may never need to think about that beyond a periodic oil change, which you can do yourself.
It looks like any of these choices will have the slight disadvantage of making a rear tire repair a bit of a fuss. Whatever you get, just rehearse a tire change at home a couple times.
Sucks bilgewater having your custom-kitted bike stolen; I lost two in about a year and a half. The bikes themselves weren't very special, but I had them fully equipped, which added substantially to the loss. Best of luck with your new ride.
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