"We have stratum zero at home"

A rubidium clock you pace to the BPIM, thats stratum 0. A clock you sync to the GPS system, which itself is under very indirect management and has some very specific time drift issues to various forms of civil and scientific time... I am less sure is a stratum-0. You don't own the time source, you get to read it.

Mostly, the ones I have been involved in have being training a PPM signal off the GPS source, and have minor issues around the kernel timing to read the serial train. That only limits precision. You still have the usual issues with your hosts crystal synced clock, and I've read a bit of stuff which suggests RPI are not very good in that regard. And, USB is not a very good basis for regular, reliable paced reads. There are projects which expose the PPS on other lines in the GPIO pins, I don't know how well that works (or even, how it's achieved given the USB pinouts available)

I run an instance of Bert Huberts GPS tracking project with a ublox USB thing, and another instance of a newer UBLOX antenna, on a NUC doing chrony. In the past I ran a number of the RIPE NCC serial GPS cards in Dell servers.