My experience at home is using Biburo(free) for windows http://tokeiyade.michikusa.jp/download/
with wine on Ubuntu Linux. I needed to use a cheap 9v battery guitar preamp and piezo disc from a broken toy as mic to regulate my dive watch.
I have built a few of these watches as gifts and I can get it to within 1-4sec fast after they have been worn in for at least two months. The miyota is a pain to regulate as it just has a swing bar not a screw, having a regulating machine of some sort makes nudging it into position easier than bumping back and forth over a period of a few days.
I have heard that some people solder a clip to the piezo disc mic and can get a good takeoff by clipping to the stem(unscrewed crown?) though this would probably require taking out the case clamps and removing the movement. My old pocket watch and stopwatches would probably work with the Nokia hands free mic though.
Even so a regulating app, even if it requires a cheap preamp, would be nice even to be sure that the (forget tech term here) outer hairspring center adjust is correct if at an antique show.

Then thinking about putting the audio theough a time calibrated wave scope puts me in mind of making a ECG(heart electricity waveform monitor) that converts the output to sound readable by the phone app, or an oscilloscope for goofing with radios, though I dont think the sample rate is high enough.