First of all, puppies bite. In the beginning (at the stage you are now) it's due to play and/or tasting the world. He will lose his puppy teeth when he's around 4-6 months old, and at this point he will start biting (and chewing) due to his gums itching and hurting. Most puppies are done with biting when they get their new teeth if they've had consistent training.
Cujo moments are, as you've guessed, usually in connection to the puppy getting overly tired or over-stimulated. Or just over-excited because they're happy, or because they just pooped or peed. Just like human children, they get hyper and make a lot of noise, do things they're not allowed to do, and generally make us crazy. If you see it coming, you can usually distract them and calm them down with nosework, like sniffing mats, or calm treat toys.
Now, some puppies bite more than others. I've had an extreme biter, and if you screamed, said "no!" or pushed her away, it triggered her to bite harder. Much harder. I see you mention timeouts. That's a good idea, but if you move the puppy to a timeout zone, it's slow, you have to give it attention by picking him up, and your puppy might not even make the connection. The simplest way is to actively ignore. You need to teach the puppy that biting = boring, and it's a simpler way of doing timeout.
If you are playing with the puppy on the floor and he bites, immediately stand up, turn away from him, cross your arms over your chest (to discourage jumping) and look up at the ceiling. Never angry, just calm and demonstrative until he stops and relaxes (or goes away). If he's biting on the lap, put him down, stand up and do the same thing. If you're walking across the floor, stop and do the same. Biting = boring.
The difficult bit is to be consistent. Everyone in the household has to do this, and if you react to his biting, he wins. Getting a reaction is play to him. So put on old clothes so that you don't worry about them being ruined, put on shoes or boots so he can't hurt your feet when biting, and wear jeans or pants that protect your legs from pain as well.
This is not needed for every single puppy, but my parents had an extreme biter. Took 10 months to get her to stop biting. The reason was that my mother and sister refused to wear "protective" clothes, so they often reacted or kept walking if they crossed the floor and she "attacked." Sometimes because she hurt them, sometimes because they were worried about ruining their pretty clothes, and sometimes because they were in a hurry. My father and I dressed for the biting as soon as we got home, and always took the time, even if we had to stand still for 10 minutes. She completely stopped biting the two of us when she was around 5 months old.
So to sum it up: he will bite you to some extent until he gets his adult teeth between at 4 and 6 months. You will be able to reduce his biting before then if you train him, but there's a good chance you won't see any results for a couple of weeks, and even then he will still forget himself sometimes. If you keep changing methods because you don't see results after a few days, you won't get anywhere. It's not just about training, though. He's a baby, and he needs to gain the mental capacity to make the connection between his behavior and your response.
I've had 6 puppies in 20+ years of being a dog owner, and I've cried in regret every single time. I've felt upset, exhausted and scared that I'm not able to handle it. That I don't want my life to be like this. I have a 13 week old puppy right now, and I cried last week! But it's temporary. I made a choice, adopted a puppy, and I have to be strong enough to make sure I'm her forever home. It will be okay, it will get a little easier every week, and I just have to hang in there. I can do it, and so can you. Don't think that someone else can do it better than you, because that's not true. You CAN do this, I promise. If you've already managed to teach him 3 simple tricks, then you have the skills. All you need now is patience, and as long as you remember that puppyhood is temporary, it's a lot easier to handle the frustrating parts.