Wouldn't blessing a copy of the reference in order to extract the address work, and allow the blessed copy to be discarded leaving the original unmodified?

Nope. Blessedness is associated with the referent not the reference. For example:

use Test::More 'no_plan';

my $original = bless {}, 'Something';
isa_ok $original, 'Something';

my $copy = $original;
bless $copy, 'SomethingElse';

isa_ok $original, 'SomethingElse';

__END__

ok 1 - The object isa Something
ok 2 - The object isa SomethingElse
1..2
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