First it is important to know that this kind of screaming is normal for the dog. Very young puppies will scream continuously when separated from the litter. That behaviour evolves but it makes sense for the dog: being reunited with his social group. So don't get angry or too nervous and don't resent the dog, he is not doing that to challenge your sanity (writing this also helps trying to convince myself...).
Next thing is about elimination: depending on the dog (I don't know if Shiba's have special need in this case) 11 weeks can be too young to have complete control. In the morning he might actually need to pee / poop.
So that's about prevention.
Then comes training. Training should not take place at 6am when you're half asleep, concerned about the noise, etc. You should train him when you're calm and relaxed and when all his needs are met (eg. elimination).
It is good to ignore him. Cesar's "no touch no talk no eye contact" is quite valid in this case. Just ignore him. Do not reward bad behaviour, referring to my first two points, do not punish them either (technically the removal of your attention is a negative punishment: you punish him by removing something he wants).
However that's only one part. You need to also teach him what is the good thing. You need to positively reinforce his good behaviours. Basically you could crate him anytime in the day and reward his calmness and the absence of barking. Do not hesitate to reward a lot at the beginning, rewards every tiny steps. You can also add distractions, invent situations that are more likely to make him bark (ask another person to get out of the house, ring the bell, come in, etc.).
You can reward him in the crate (food reward is maybe the most practical solution in this case), or the reward can be to be let out of the crate and play with you (I would do a few repetitions of the first and end with the second option).
As the dog will understand what's expected from him, increase the time between the rewards, and start rewarding only when the dog is actually calm! The dog can be overexcited but sitting and not barking. That's not what you want to reward, however sitting is a first step (and can be rewarded at first) and it helps the dog to relax.
Quoting Karen Overall "Manual of Clinical Behavioral Medicine for Dogs and Cats" book:
The single most important step in the treatment of any of these dogs is also the most commonly skipped step: reward the dog whenever the dog is calm, even if this calmness is spontaneous and not requested by you. The more relaxed behaviours you can encourage the dog to incorporate into daily life, the better off everyone will be. This means that you should even reward the dog when he is sleeping or napping as these are variants of calm behaviours.
(emphasis and typos are mine)
This is in the context of treating dogs with separation anxiety. This is not exactly your case here, but that part certainly applies.
The goal is then to actively reward the dog. Not to setup situations where he could fail. To rule out the possibility that 7 hours is too long for him (second paragraph), try (once or twice during a week-end) to wake up after only 5 hours, when he's not barking, let him pee and go back to sleep.
