I have a tiny Olympus Voice Recorder. When I need down-to-the-second timings, I conceit on my person (In 2 party states it will then not pick up the other person's voice clearly). At crucial time in the interaction I will say things like, And good morning to you," marking when they greeted me, and parroting exactly what they said.
It has a retractable USP connection. I can extend that to plug it into my computer, where it displays second-to-second my voice clues. Granted, I do very, very few "timing" shops, and this might be time consuming to scan thru to write a report. But, that recording is a very tangible proof of the timings. If I recall correctly, I got the recorder for about $24 at Best Buy. Try re-sellers for used ones.
Based in MD, near DC
Shopping from the Carolinas to New York
Have video cam; will travel
Poor customer service? Don't get mad; get video.