Sounds like fun! For what it's worth, ublox GPS modules and their clones should be configurable to always produce a PPS signal regardless of whether or not they have a satellite fix. The module would probably do a better job than software on a pi could during transient periods without a fix (due to how accurate the oscillators need to be in a GPS module). So, as long as you can trust the GPS module to exist and be powered, you should be able to reliably clock your display update with it. The only reason really to generate your own PPS would be if you want it to work without a GPS module at all, perhaps by NTP or something; you're then of course again looking at only a millisecond or so of accuracy.
I'm using an uputronics GPS/RTC hat that has a u-blox M8 engine. I set it to stationary mode for extra accuracy. I'll have to look into other configuration options.