That sounds so tough and I can see how difficult it is for all of you.
I'm a real believer in "all behaviour is communication" and I'm wondering what is behind his "tantrums"? What you say about cuddling him until he fell asleep, exhausted, sounds to me as if they are different from typical toddler tantrums and more like a meltdown where everything is simply too overwhelming for him.
Try "being a detective" to see what might be triggering the tantrums/meltdowns.
Could he be reacting to his sensory environment- too hot, too cold, too bright, too noisy? Clothes too itchy or too tight? I know you've got building work going on, but can you find a quiet part of the house where he can escape to/encourage him to go if everything seems to be getting a bit too much? Does he have a trampoline or swing which can provide sensory input if he craves that?
Does he struggle with transitions from one activity to another? Try a very simple picture board with pictures of the daily activities- breakfast, brush teeth, get dressed, play time, go to shops/park, lunchtime etc. You could also try a "now and next" board- now you are eating lunch, next you will go outside to play.
Use very simple verbal instructions. Instead of saying "we're going to go to the park in a minute, finish up your lunch, then go to the toilet and put your shoes on", break it down into stages.
If he does have a tantrum/meltdown, make sure he is safe, with nothing nearby that could topple over or hurt him, then try sitting quietly nearby. Try to stay calm and quiet. As you have found, giving cuddles might sometimes calm him.
All of these are strategies I have used with my daughter who is diagnosed with autism. She had meltdowns lasting 3 or 4 hours when she was your son's age.
I'm not saying that your son might be autistic, but give these strategies a go. They won't do any harm if he is not autistic, but they might help to improve things around the home.