Is there a safe "latchable" way to cut power to SD cards on a data logger?

Your datasheet values are for SDIO mode with a 25 MHz clock.

However, in order to achieve the lowest sleep current, the host needs to shut down its
clock to the card.

The above is from your datasheet.

In SPI mode with no clock you can achieve very low sleep current.

I did these tests with a Teensy 3.1. It has a 3.3 V regulator and I measured 3.2766 V with a Fluke 287 meter.

These are standard size SanDisk cards with unused pins high through 10K resistors.

I started with an old SanDisk 1 GB card. I ran the the SdFat SdInfo sketch and measured current to the SD with the Fluke.

Manufacturer ID: 0X3
OEM ID: SD
Product: SD01G
Version: 8.0
Serial number: 0XFB5C4F70
Manufacturing date: 12/2006

cardSize: 1015.81 MB (MB = 1,000,000 bytes)
flashEraseSize: 32 blocks
eraseSingleBlock: true

The current after inserting the card was 66.1 micro-amps. After running SdInfo 65.8 micro-amps.

A newer SanDisk 4 GB class 4 SDHC card.

Manufacturer ID: 0X3
OEM ID: SD
Product: SU04G
Version: 8.0
Serial number: 0X3F6E5C18
Manufacturing date: 6/2012

cardSize: 3965.19 MB (MB = 1,000,000 bytes)
flashEraseSize: 128 blocks
eraseSingleBlock: true

Before init 77.9 micro-amps and after SdInfo 69.9 micro-amps.

Here is a SandDisk 4 GB class 4 card with higher current.

Manufacturer ID: 0X3
OEM ID: SD
Product: SU04G
Version: 8.0
Serial number: 0X4E728B0
Manufacturing date: 10/2013

cardSize: 3965.19 MB (MB = 1,000,000 bytes)
flashEraseSize: 128 blocks
eraseSingleBlock: true

Before 104.6 micro-amps after 108.4 micro-amps.

Here is a high end Samsung Pro 16 GB microSDHC www.amazon.com/Samsung-Electronics-Adapter-MB-MG32DA-AM/dp/B00IVPU894

Manufacturer ID: 0X1B
OEM ID: SM
Product: 00000
Version: 1.0
Serial number: 0X9B541463
Manufacturing date: 3/2014

cardSize: 16003.89 MB (MB = 1,000,000 bytes)
flashEraseSize: 128 blocks
eraseSingleBlock: true

before 92.3 after 89.8