I hadn't seen the STM32F072; it does look quite attractive. Thanks for the info.
As you say, the ideal thing would just be to have the Edison connect directly to the microSD card. Unfortunately there doesn't seem to be any really good way of doing that, especially if you want to be able to drop back down to 1.8V signalling (for the high-speed modes) after initialisation.
If there was a way to limit the Edison's SD peripheral to just using SPI mode then I'd probably do that. Slow, but level conversion costs virtually nothing for SPI (three low-to-high converters and a resistor voltage divider) and I'm not planning to boot from microSD very often. Unfortunately, without a full datasheet for the chip it's pretty much impossible to check whether that can be done.
Perhaps one of Intel's representatives could explain the "correct" approach? Surely they've built a couple of boards with SD sockets for testing.
Edit: with a lot of further research, it looks like the TI TXS0108 will do the job. My understanding is that the clock line has to be fed back through the chip to connect to the CLK_FB pin on the Edison. The TXS0108 is both cheap and (relatively) easy to solder.