When I open the door Duco is always very excited. After a while he stops barking but he is almost continuously whining. Sometimes he redirects on the leash or towards me.

This is a common issue. Kudos to you for being pro-active and putting a muzzle on him. 

I would suggest treating this as a training exercise in and of itself. Start by just waiting him out until he is not barking, then move forward. Do lot's of repetition of back and forth/in and out until he starts relaxing. The repetition will help break the conditioning cycle that every time the door opens he is going out for a walk. Practice this a lot even when he you aren't going to walk him. Also practice when you are not in a rush to be anywhere/do anything so that you can really wait him out until he is calm. 

The other thing I would do is try rewarding with food when he is sitting without barking, even if he is whining. The whining generally is a byproduct of frustration, the more you reward him in that position, the more content and less frustrated he should become and hopefully the whining will subside. 

If he starts getting real worked up, or trying to break and move forward before given permission, then I would correct him with a steady upward pressure on the leash. Try not to pop the leash as it may cause him to get more worked up/redirect. Hold the pressure up until he relaxes, then give a big, active release.