Your override can be written more simply:

my %obj_cache;

override 'new' => sub {
    my ( $class, @args ) = @_;
    my $params = $class->BUILDARGS(@args);
    $obj_cache{$params->{thingy}} ||= $class->_new($params);
};
[download]

As you're potentially not creating a new object, but returning a cached object, I don't think Class->instance(%args) is a bad name for the method call. new would be a misnomer.

What if I change my mind about caching, or want to debug the code without the cache? Then I have to find all the calls in all my code and change them.

No, you wouldn't need to change all the calls. You'd just need to change the instance method to always return a new object:

sub instance { shift->new(@_) }
[download]

One of the things I'm encouraging in Zydeco is the idea that the new method should be considered internal to the class, and the class should provide factory methods for external code to call. And it's for this kind of reason — it allows the class to do things like return cached objects, or a singleton, or whatever.