Having a look at the migrate_server script i see the option -skip_logs inside.
Did you try
$FWDIR/scripts/migrate_server export -v R82 -skip_logs /var/log/ExportedDatabase.tgz
I can't do that myself at the moment due to a lack of lab facilities, and I'd rather not touch our productive management system.
Edith explains:
Variable definition:
migrate_args="-ma "
has_migrate_args=0
include_log_indexes=0
skip_logs=0
logs_flag_provided=0
And argument parser:
-skip_upgrade_tools_check)
no_upgrade_tools_check=1
;;
-skip_logs)
skip_logs=1
;;
-[lx])
logs_flag_provided=1
and now to something completely different - CCVS, CCAS, CCTE, CCCS, CCSM elite