You can pipe the output of a cron job to a file easily enough - https://www.thegeekstuff.com/2012/07/crontab-log/
Clearing the cache is a pretty common thing to do in troubleshooting Mautic, it is generally the first step. It should have been cleared by the migration script in the last step of the migration - did it perhaps show a message in that step saying that it was unable to complete?
Glad to hear you got to the bottom of it!