You need a TCXO or OCXO as part of a GPSDO. A GPSDO works by tweaking the oscillator up or down, depending on a phase or frequency measurement performed anywhere between 1 sec and several minute intervals. In effect, it's a very slow phase or frequency locked loop. That means that the noise, jitter, spurs, and junk produced by the oscillator will appear directly on the GPSDO output signal. If you start with a dirty oscillator, you end up with a dirty output, no matter how elaborate your GPSDO design. Try running some test equipment with an external reference signal that has a mess of 60 Hz FM noise on it, and see how far you get. Think of the FM noise as producing "uncertainty" in any measurement.
I don't understand what you mean by "external" TCXO. You can put the TXCO anywhere, but if it's part of the GPSDO loop, it has to operate as part of the system.
Ultimately, most frequency references either talk to a time service, or have a built in atomic reference available. Those references are transferred to your TCXO and OCXO which in turn produces your output. You could probably build something based on the transit of the moons of Jupiter, but I don't think you have the R&D budget.
Drivel: Speaking of a noisy reference, I had an AC power ground loop problem as parts of the building were on different AC power grounds. I could produce a substantial spark when connecting coax grounds that ran between buildings. There was also an RF leak that superimposed a local AM radio station onto the 10 MHz reference signal. Since I was doing the bulk of the complaining, I was soon sentenced to fix the problem (late at night, so I wouldn't disrupt production). The company distributed the 10 MHz reference signal over a fairly large area, through hundreds of feet of variable quality coax, to assorted test equipment, some of with had the external reference shield at case ground. In order to fix this, I added home made isolation xformers and filters at each station. I also built several distribution amplifiers so that some idiot (i.e. me) would not shut down the entire company by accidentally shorting the reference signal to ground. I also made a feeble attempt to properly terminate the cables at 50 ohms, but that was futile due to the large number of T connectors in the system. I almost forgot to mention replacing about 50+ badly soldered BNC connectors with crimp BNC.