I spent this evening building a prototype. I used a board for my GPSDO clock accessory, left off the microcontroller and tacked wires on to bring +5 from the Pi along with MOSI, CLK and !CS from the GPIO header.

The result took some horsing around to get working.

I found I had to not only enable SPI, but I had to add

dtoverlay=spi0-hw-cs

or else the CS line wouldn't work properly. I'm not entirely sure I understand why, but the hardware CS system works and the software one doesn't. Go figure.

But that done, when I take a slow-mo video to compare the result with one of my GPS clocks, it's (at the moment) about one frame slow, which easily puts it under 10 ms. With this prototype, I'm cheating a little - it happens to be one of my stratum 1 public servers, so it actually has a GPS module connected up to NTP, so I know that the actual Unix clock is well under a few dozen microseconds accurate. In short, the clock is performing well up to the desired specification.

Now it's just a matter of waiting for boards to arrive from OSHPark and a Pi Zero W from whichever vendor happens to ship first. :)