New Horizons images enable first test of interstellar navigation

That's a remarkable result. Looks like (if I haven't misunderstood) SEXTANT a software experiment that piggybacks on the raw datastream from the NICER x-ray telescope, and estimates the phases of the time-of-arrival of bright millisecond pulsars (in x-ray photons). From differential phases (at microsecond accuracy), they infer differential position (kilometers). I understand it's eight (8) pulsars in the catalog.

https://arxiv.org/abs/1711.08507

I wonder if it's really that easy to extend this to interstellar scales. If you move 300 km, a 1-ms source is reset to its original phase. Go out to New Horizons distances, and all your phases are millions of cycles offset from Earth, by highly jumbled fractional parts. Is it mathematically feasible to reconstruct everything then? Or: do you maintain a continuously-updated model across the entire mission—and hope that you don't lose count of your cycles?

That paper says this kind of pulsar can be as slow as several seconds, and the main discussion link says the parallax navigation could be made a lot better with a better camera. Maybe that could provide enough overlap?