Your .sig also applies to me, so with the caveat that I could easily be wrong, its my impression that we really can't be as precise as we would hope for without "the averaging function" implemented in some robust way, with GPS.
Because the ionosphere, temperatures changing, tidal forces changing the gravity minutely, and things like that.
Think of the simplest aspect of GPS as simply a set of clocks very precise clocks synchronized to one another in space. And then they stream it over radio, using a technology that let even very weak signals be pulled up out of the noise, (its typically below the noise!) by the magic of statistics.
At precise intervals that streamed time as broadcast by the satellites in view is recorded, bang, bang bang. and from that (and trigonometry) is derived the distances to them at that instant.
Then the position of those satellites at that instant is known to an arbitrary precision we then can get the time back, minus some variability which also can be calculated.
All the errors add up. One error that changes a lot is the ionospheric factor which to me seems similar to the waves on an ocean and which seems similarly unpredictable.
However if you have a stationary "base station" nearby you know the position of, and you can combine -subtract its position from your data stream you get a difference figure that is more accurate positionally. Similarly if you know that you yourself are stationary, and the GPS can be told exacly where it is and store that (One way of doing this is called "TRAIM" thats probably what your GPSDO is doing)
With TRAIM you can get a substantially more accurate signal than otherwise for timing purposes.
How does it work? Your GPS is stationary and you know that, and can tell it that,
It itself then using statistics can figure out the location in a way that (should) get steadily better the longer it is turned on. But at some point (which should be a long time, >24 hours is optimal) it reaches a point of diminishing returns.
THEN say its figured out where you are -and has stored that position..and the signal is very good, then it can give you a timing signal that it knows is quite accurate. verifiable quality. It only needs one satellites signal at that point, to do that.
But anyway, all GPS's fine tune their internal settings to give you the best possible solution that's available given the information that they have available.
Just using ephemeris data that the satellites themselves provide that may be very good.
You can get timing accuracy to under ~100 nanoseconds from virtually all good GPS devices - but that accuracy can easily be lost in the signal chain - after it leaves the GPS, for example, interrupts and the servicing of them. Or the cable delay which should be stable, that you can compensate for.
Many GPSs are substantially better than that, but the accuracy they claim is only under ideal other conditions which dont exist in the real world.
There is this substantial variability due to these other factors which is unavoidable but which does occur in somewhat predictable ways.
Those same things would effect timing. You can minimize one of them, multipath, by setting a very high elevation mask and using an antenna that rejects the wrong polarization, no-matter what direction its coming from (because signals that are reflected once are reversed polarity).
But even if your setup is totally optimal to do much better, orders of magnitude better, you need a way of averaging the time out - over time. You can get another order of magnitude or maybe even two fairly easily, by disciplining an ovened quartz oscillator. That's still much better than anything we could do as little as 25 years ago. Even if your device has the best GPS signal there are things which it may be unable to cancel out which could be improved on by thermal controlling its environment.
Also, barometric pressure influences crystal oscillators measurably.
Still where we are now is a pretty amazing place.
You may be able to get better performance by controlling your oscillators temperature precisely. I don't know. But you may not need that now or in the near future, whats the point?
If your device does what you need it to do, gives you a precise, plug and play source of different frequencies for testing, it was likely a better choice for you than an ovened GSDO.
I know I don't need that level of precision in anything I currently do, yet.
But I hope to eventually. Many applications, for example in telecommunications, need more.
The more mileage they try to get out of the spectrum, the more timing precision they'll need.
So I figured I could use it someday, maybe.