I think you are storing a reference to that registry, and not a "deep copy" of the contents of the registry. Try this (I can't test b/c no Win here):

use strict;
use Storable q(dclone);
use Win32::TieRegistry ( Delimiter=>"/", ArrayValues=>0 );
#snapshot registry before install

my $LmRegBefore = dclone $Registry->{"LMachine/Software/"};

#Run the installation program - much harder in real life, but this is 
+a test script :)
my $install='path to install to run';
system($install);

#Flush the reg subkey
my $r=$Registry->{"LMachine/Software/"}->Flush();
print ("Flushing LMachine[$r]");

#snapshot registry after install
my $LmRegAfter = dclone $Registry->{"LMachine/Software/"};

registryChanges($LmRegBefore,$LmRegAfter);
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