This is one of those occasions when the intelligence in one module (Storable) combines with the incompleteness of another (threads::shared), to produce a mess.

Your JSON cloning mechanism is overkill though. A simple dumb clone() does the trick:

#! perl -slw
use strict;
use Data::Dump qw[ pp ]; $Data::Dump::WIDTH = 1000;
use threads;
use threads::shared;
use Storable qw[ store retrieve ];

sub clone {
    my $ref = shift;
    ref( $ref ) or return $ref;
    ref( $ref ) eq 'SCALAR' 
        and return \(''.$$ref);
    ref( $ref ) eq 'HASH'   
        and return { map+( $_, clone( $ref->{$_} )), keys  %{ $ref } }
+;
    ref( $ref ) eq 'ARRAY'  
        and return [ map       clone( $ref->[$_] ) , 0 .. $#{ $ref } ]
+;
    die;
}

my %hash : shared = (
    letters => shared_clone( { 'a'..'z' } ),
    numbers => shared_clone( { 1 .. 100 } ),
);

store clone( \%hash ), "$0.bin";
my $retrieved :shared = shared_clone( retrieve "$0.bin" );

pp $retrieved;
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