Возможно перл:
perl -MTime::Piece -i.bak -pe '
if ( /([[:upper:]][[:lower:]]{2} \d{2} \d{4} \d\d:\d\d:\d\d)/ ) {
$datetime = Time::Piece->strptime($1, "%b %d %Y %T");
$epoch = $datetime->epoch;
s/$timestamp/$epoch/
}
' log_file