I wanted to get around using explicit accessor and mutator methods and simply have a subroutine which, with a little syntactic sugar, could be used as a variable.

Then you should take a look at Lvalue subroutines.

By way of example here are a couple of classes that use lvalue method ->item():

package Vector {

    sub new{ my $class = shift; bless [ map{ int() == 0+$_ ? int() : d
+ie( "'$_' not an integer in Vector::new" ) } @_ ], $class  }

    sub item :lvalue { $_[0]->[ $_[1] ] }

    1;
}

package Matrix {

    sub new { my $class = shift; bless [ map{ ref() eq 'Vector' ? $_ :
+ die "'$_' not a Vector in Matrix::new" } @_ ], $class }

    sub item :lvalue { $_[0]->[ $_[1] ]->item( $_[2] ); }

    sub mmMxN {
        use integer;
        my( $self, $other ) = @_;
        die "Incompatible matrix dimensions" unless @{ $self } == @{ $
+other->[0] };

        my $return = Matrix->new( map Vector->new( (0) x @{ $self } ),
+ 0 .. $#{ $other->[ 0 ] } );

        for my $i ( 0 .. $#{ $self } ) {
            for my $j ( 0 .. $#{ $other->[0] } ) {

                $return->item( $i, $j ) += $self->item( $i, $_ ) * $ot
+her->item( $_, $j ) for 0 .. $#{ $other };
            }
        }
        return $return;
    }
    1;
}
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