I don't like the way you have to declare a checked variable:

$intfactory->Monitor(\ my $var) = 42;
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Yes that's ugly. You can at least get rid of the backslash. $_[1] paseed to the method is an alias to $var so \$_[1] is \$var.

Note also that the value of a scalar assignment is itself an lvalue.

sub Monitor : lvalue {
    my CheckFactory $self = shift;
    my $rvar = \shift;
    my $lvar = $$rvar;
    tie $$rvar, 'Checkee', $self->{Closure};
    $$rvar = $lvar;
    $$rvar;
}

$intfactory->Monitor(my $var = 42);
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If you want more syntactic sugar then take a look at attributes.