Run coercions inside a Type::Tiny custom constraint?

I have a custom DateTime type that has a coercion defined on it from string to DateTime, like so:

package Library;
use Type::Library -base, -declare => qw(DateTime);
use DateTime::Format::ISO8601;

class_type DateTime, { class => 'DateTime' };

coerce DateTime, from Str, via { DateTime::Format::ISO8601->parse_datetime($_) };

I'd like to use that DateTime type in a Dict, like so:

package MyObj;
use Moo;
$constraint = declare MyType, as Dict[ name => Str, date => DateTime ];

has 'whatsis' => ( is => 'ro', isa => $constraint );

And then call it as:

use MyObj;
my $obj = MyObj->new( whatsis => { name => 'Something', date => '2016-01-01' } );

I've tried adding coerce => 1 to the declaration of whatsis, but that did no good.

How do I create a custom type that inherits from Dict and runs the type coercions defined on the member types?

With lots of help from https://metacpan.org/pod/distribution/Type-Tiny/lib/Type/Tiny/Manual/Coercions.pod

Library.pm:

package Library;
use Type::Library -base, -declare => qw(Datetime);
use Type::Utils -all;
use Types::Standard -all;
use DateTime::Format::ISO8601;

class_type Datetime, { class => 'DateTime' };
coerce Datetime,
  from Str, via { DateTime::Format::ISO8601->parse_datetime($_) };

declare 'MyType', as Dict[ name => Str, date => Datetime ], coercion => 1;

MyObj.pm:

package MyObj;
use Moo;
use Library -all;

has 'whatsis' => ( is => 'ro', isa => MyType, coerce => 1 );

tester.pl:

#!perl
use MyObj;
my $obj = MyObj->new( whatsis => { name => 'Something', date => '2016-01-01' } );
use Data::Dumper; print Dumper $obj;