Since it was the same Lucene index file that was being reopened and never closed, I thought the indexes might be fouled up.
1) I shutdown Alfresco.
2) I changed alfresco-global.properties: index.recovery.mode=FULL
3) I deleted /opt/alfresco/alf_data/lucene-indexes directory.
4) I restarted Alfresco.
5) I changed alfresco-global.properties index.recovery.mode back to AUTO, since I don't want it to re-index on any subsequent restarts of Alfresco.
I don't have conclusive proof of what happened to foul up the index, but I have a theory. So, take it with a grain of salt:
I'm assuming that when I first started after the upgrade that, when the number of open files reached the system max per process (was set at 1024), something in the index got askew. So, even after I raised the linux system limit for open files, the index needed fixing.