Attached is what I ended up with. I used the advice of the other users to (1) change my DAQmx read VI to "Single Sample Waveform" and (2) used a wait (ms) function in a flat sequence with a DAQmx stop VI followed by a play VI in the subsequent frame. I'm sure there's a simpler way to do this, but this worked for me. Loop times are consistently 25 seconds (20 seconds acquisition and 5 seconds rest) between trial loops.
The last paragraph of the Solution gives two methods to fix this (I know, because I wrote it ...). Sometimes a Thousand Words (well, a few hundred) are Worth More than a PNG, particularly if you are trying to teach someone how to "Think LabVIEW".