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use strict;
use warnings;
...

Now with just the minimal URL, I get the same error:
Error GETing https://contests.arrl.org/: Can't connect to contests.arr
+l.org:443 (Bad file descriptor)

my $mech = WWW::Mechanize->new( autocheck => 1, 
                                ssl_opts => { verify_hostname => 0}, )
+;