Revisiting this issue:

While under the hood today I noticed powdery-white corrosion on the bolt-down plate that secures the battery, and some additional corrosion on the positive terminal. I removed battery, cleaned/scoured away all visible corrosion, and replaced it.

Upon starting the car it fired up very strongly and the tach, instead of surging a bit as it typically has been doing, remained locked in the 1000 rpm range. Upon driving off, the anticipated "first start of the day" ASR fault did not occur.

It’s too premature to say for sure the ASR problem was a voltage issue all along, but I’ll chime in again after a week or so if it does not return. Nonetheless, it probably is/was electrical, with the NSS playing a role.

7/27 Update:
Still no ASR faults.

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2008 E350 4matic / Black/Anthracite

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Gone but not Forgotten:
2001 E430 4matic, 206,xxx miles, Black/Charcoal
1995 E320, 252,xxx miles, Black/Grey
1989 260E, 223,00 miles, Black/Black