Use coercion in your attributes in Funky::Rectangle.

package Funky::Rectangle;
use Moose;
use Types::Standard qw(InstanceOf Str);
use Data::Dump 'pp';

my $vertex_type = InstanceOf->of('Funky::Vertex')->plus_constructors(S
+tr, "new");

has 'LL' => (is=>'rw', isa=>$vertex_type, coerce=>1);
has 'UR' => (is=>'rw', isa=>$vertex_type, coerce=>1);

# ...
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Update: note that this can be achieved using Moose's built-in type constraints, but adding coercions to those has a global effect which can result in spooky action at a distance.