I promised to be back when I got my ZOOM R16 to report how to create overdubbed recordings. This task is quite simple, as R16 starts the counter of the first track to record at time 0.000s and creates a corresponding wav file. To start the next track to record (together with the corresponding next wav file) just go back to this start time. The R16 project collects all overdubbed recorded files, and they all start at the very same time 0.000s, with millisecond accuracy. Importing the files (one after another) in one and the same audacity project, cursor position at start time, gives the correct ensemble play of all files.
I am very happy my problem of multitrack recording is solved by using R16 and I can continue to use the excellent facilities of audacity for editing every single file.