With the Beaglebone, it's theoretically possible to drive the oscillator from a calibrated clock source (use the PPS pulse to discipline an oscillator). I was too lazy to build such a circuit and observe the effects. Some uBlox timing GPSes let you output a suitable signal (you can adjust the frequency in software), but the adjustability range when I last checked wasn't enough to make it work for the Beaglebone. Once you have the MCU running at a well-defined and stable frequency, I think it's possible to give Linux extremely accurate data, or at least know which clock cycle was the start of a second. I don't actually know how much any of this will help, and it's honestly not within my capability to measure.

For me, the outcome of my GPS clock project is that I never have to set my clock, and it looks really good. Running "chronyc sources" is always pleasurable as well, but I probably wouldn't notice a clock that's 20ms off unless I was comparing it against WWVB or something.