What do you get if you widen the subscribed topic?
Currently it is...
if (!client.subscribe("$aws/things/chicken-door/shadow/name/door/#"));
but do you get more if it is changed to...
if (!client.subscribe("$aws/things/chicken-door/shadow/#"));
Maybe it is not coming in exactly as/where you hoped.
Another thing to try is commenting out the sendData() lines in loop and see if you do eventually get a reply to the getShadow() in setup. The pubsub library may need to do a few client.loop() calls before the AWS reply comes in and maybe the sendData() is stopping the reply.