Then you could use a pseudo-object, for example storing your global variables in a lexical hashref in the const module, and have in that same module a get and a set functions to access the hash that you export. Something like this:

use strict;
use warnings;
use Exporter;

our @ISA = 'Exporter';
our @EXPORT = qw(get set);

my $private_hash_ref = {VAR1 => "one", VAR2 => "two"};

sub get { my $key = shift; return $private_hash_ref->{$key};}
sub set { my ($key, $value) = @_; $private_hash_ref->{$key} = $value;}
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And then in your main code or other module, you just use the set and get functions.