I know this is a late reply, but:
all, the mentioned apps are simply comparing to local/remote time signals over long periods (days, weeks?).
Why not check the mechanical movement directly via acoustic pickup by microphone, in real time? To obtain results within one to two minutes instead of days? Only then an adjustment or regulation of the mechanism can be done efficiently.
"TickoPrint" (Android) clocks the mechanical noise in real time, shows envelopes, angles, calculates the daily drift, and plots all like the professional tools seen in watch repair shops.
I am using this software for many years now, adjust my mechanical watches with it if needed and achieve good results. I own about 100 wrist watches, from old 18000bphs up to 28.8kbphs, all are recognized automatically by the software.
To improve the functionality I constructed a little wooden bench, with a built-in microphone directly underneath.
This way I can place the watch horizontally and vertically, face up/down to check the regulation. But directly placing the watch on the device's microphone or a connected headset-mic will work as well.
An alternative, yet less intuitive and more complicated, app for frequency counting and spectral analysis is "WildSpectra Mobile". It is not intended for watch movement control, but can be tweaked to do so. One needs to carefully adjust the settings to obtain useful results and graphics..
All these apps are very accurate, dely on the device's high GHz clock frequency as reference,
Here are screenshots of both apps I am relying on.
Personally I do not see any sense in using the other 'time server' apps; atomic clock signals can be obtained directly from GPS, radio and TV stations. And Android devices can be automatically synced to the NNTP signal any time, for direct and immediate comparison of any other clock or watch in the private home.
TICKOPRINT:
WILDSPECTRA: