Just to close this thread.
We have both a solution and an explanation thanks to Michael Mulrooney of Softrak.
The problem originated 2 years ago when the "Job Cost Interface" in AR Profile was changed to "Adagio Job Cost" (likely out of curiosity) and then reset it to "ACCPAC Plus Job Cost".
When we deliberately chose "Adagio Job Cost" this week, the necessary data conversion never happened because AR thought that it had already been done.
Our client's data has been repaired by the staff at Softrak and all is operating correctly.