Hello Tom,
I am running into a similar problem with an Arduino based board I'm working on currently.
Through trial and errors and previous experience, I have determined that the SD card can stay powered through all input pins (MOSI, SCK, VCC, CS). By switching low all these pins and turning them into inputs, the card finally turns off and I measure 0V on VCC pin (otherwise ~2.9V when in sleep).
In my case, doing SD.init on it will "fail", i.e. return false, but further print to file will typically work.
That might have to do with the internal state of the SD library (also init on already initialized SD card will fail, even before turning power off). I will try to look into the SD library.
Cheers,
Robin