Yes, Thiebaud, USB is not good enough for PPS signals!
This is absolutely false.
If you are using it for NTP then GPS+PPS over USB is quite adequate (from personal experience).
Ian Lepore (RIP) who worked for Micro Semi and worked on FreeBSD did a bunch of tests on a PPS over USB setup and found it more than
acceptable for keeping a PC in (good) time. Here's the thread:https://lists.freebsd.org/pipermail/freebsd-arm/2019-August/020263.html
See if your motherboard has a true serial port - perhaps just as a header but not a back connector. If not, just set the offset of the PPS to ~10.3 milliseconds (10.3 - IIRC the offsets are in milliseconds but please check). Plus or minus 10.3, try it and see! Not perfect, but better than nothing.
You might find better results using that GPS/PPS with a Raspberry Pi as a stratum-1 server and offering that as a server on your LAN.
The next level would be something where you can do an input capture on the PPS I don't think there are any pre canned solutions. I made one with a Beagle Bone Black and a uBox GPS module but it's not exactly turn key. Or for a server then you would need a fancy (ie $$$$) internal card.
The Raspberry Pi does not have an input capture timer, but I believe you can do better with DMA hackery (I haven't tried though).