My 2 cents? I never got up at a set time to take my pup out. I put my pup in the crate and let her cry until she went to sleep. Like crzycrkr said, "You need to ignore."
Pup knows you get up the same time every morning to take him out. I took my pup out last thing, before bed. I put her in the crate. She cried the first few nights, but for less time each night, until she didn't cry anymore. I waited for her to alert me that she needed to potty. At first, the towel in her crate would be wet. Took her out anyway, to finish going. Praised. Right back in the house. Quickly wiped out crate, put in clean towel. Put pup back in crate. Went back to bed. No play time. No talking. No affection. Back in the crate. Back to bed. If she cried, I didn't come back. As she matured and could hold it, she stopped alerting me in the wee hours of the morning. That time will be here before you know it. Does your pup wet, or poop in the crate, if you don't take him out? Perhaps you should try and see what happens. Just be prepared for a clean up, if need be and don't get mad at him.
I think you have inadvertently conditioned your pup, that if he cries, you will come. Even, if you don't come, until he cries for 30 minutes - you gave in. Pup knows that if he cries long enough you will come.
Try playing some soft music on the radio for him. You MUST ignore his crying. You absolutely must, or you will not break him of this behavior. Please do not lose patience with your pup. He is a baby. If you think you are going to lose your temper to the point you will do something you will regret, please rehome the puppy. I hope you are not serious about moving the puppy to the garage. I would not even have the crate in the laundry room.
I raised three children. I remember the infant days - feeding every two hours, 24/7. The waking up and crying. Changing a million diapers and feeling sleep deprived. It's hard. No doubt. Like children, puppies are a responsibility. They are not children or puppies forever. Try to enjoy your pup.