Well, kind of minor, but:

Regarding

if ( $logfile =~ /WMS/ ) {
        $media = "wms";
        $prefix = "/usr/home/script/${media}_cust/";
        $suffix = ".$media.log";
} else {
        die "Unknown file format";
}
[download]

So, if it matches WMS, you set some variables, if not you die. Why, then, not just set the variables, then check the match and die? It's not (wholly) just golfing, I think it makes it a bit more logically clear.

$media='wms';
$prefix = "/usr/home/script/${media}_cust/";
$suffix = ".$media.log";
die "logfile name does not contain 'WMS'\n" if $logfile !~ /WMS/;
[download]

Also, is it now printing each full record whenever it starts with a digit? Or rather, is that what you're trying to do? I agree that you seem to be using $thiscust for multiple purposes -- once as the customer id and once as a file hande, and this seems unadvised.