This sounds so much like Roly - however, he tended to howl in the early hours between 3-5am, usually needing the loo. You had to admire his stamina, he could keep it up for ages

. The one time I ignored him, he pooed in his crate and then continued to howl which taught me a lesson. As he was a summer puppy I did think it was the early light mornings, but in the end it turned out to be his food making him need the loo more often during the night. Once his food was changed he was better, but we still had fairly early mornings - 5.30am to 6am. I did exactly the same as you and would wake up at the slightest wimper - very tiring and very stressful. At one point I sent him to a friend who had outdoor kennels, just so that I could get a couple of good nights sleep - when he came back he was actually a bit better and I felt better too. At kennels he could howl to his hearts content and no one would pay him any attention.
What totally solved the problem (you won't want to hear this) was when he came to sleep in my room - I get to sleep in until 7am, sometimes 8am now. However, I didn't have him sleep in my room until he was sleeping to a fairly reasonable hour downstairs (about 6am and that was with me going to bed at midnight). He will sleep downstairs now if asked, but you will get a few whimpers at bedtime and a few more in the morning at about 6.30am, but nothing too bad. He'll be two in May and if he sleeps in my room there are no problems at all. I used wonder whether it was a "boy" thing as neither of the two girls have a problem with sleeping downstairs, but now I think its just a "Roly" thing

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The things I tried were a Dap plug, snugglesafe hot water bottle wrapped in an old unwashed and recently worn T-shirt (he loved this), which to varying degrees helped.
Completely understand what its like and there is nothing worse than a cumulative lack of sleep for adding to stress levels - hope you find something that works.