I finally managed to write a program capable of tracking quartz watch accuracy with close to millisecond resolution. NTP time is the source and second hand movement of watch is the input.
Graph shows results after first two days. Black circles are measurements. There seems to be a saw-tooth pattern in AQ4030's time keeping. The movement clocks with an error of about 11 SPY, but every ~24 hours corrects the error somewhat to be closer to 6.8 SPY on average.