To review packet overviews of SNORT alerts without including all the packet headers, which can result in excessively large files, the engineer should modify the output module rule to use the "alert_fast" option. This option allows SNORT to log alerts in a 'fast' format, which includes the timestamp, alert message, and the IP addresses and ports involved, but omits the packet headers. The correct syntax for this action would be output alert_fast: output filename, where 'filename' is the desired name for the alert log file.