Can you predict when he is about to get into one of his "biting fits"? If so that would be the best time to act on it, before he really starts with biting but is just beginning to act revved up. That's when you want to get out a toy and PLAY with the dog with the toy, that way he learns what to do with those urges. Up until now when he wanted to play he started biting his littermates, how should he know it's any different with humans? So from now on when he gets playful urges a toy needs to be right there, right away.
Rotate his toys so that he does not get bored. Have 9 or so toys (or more if you can find a place for them) of different types and leave out three or so at a time, after a couple of weeks those toys go away and the next three come out.
Tug is a fine game, I don't know how to play with toys without playing tug actually. I mean fetch works for some dogs, if they bring it back...but it doesn't get out that biting and feisty predator behavior like tug does, which is what he sounds like he is using you for instead. So play tug, just remember that if his teeth land on you instead of the toy-game over.
If you fail to predict that his biting is coming until it's too late get up and leave immediately. Time outs in a certain area can work for many dogs but it has it's down sides and does not sound right for your dog. One reason is that it is not immediate, you have to waste time bringing the dog to time out. Another reason is the dog may try to avoid being brought to time out, which I think is already happening with your dog. Some dogs may dig in their heels, some may try and run away and some growl (like yours). Any dogs who hates the time out enough may progress to this point, or even to biting. Being brought to time out is confrontational, much like dragging a dog off the couch (much better to teach an "off" command using positive reinforcement, so he gets off willingly) and can cause serious problems if the dog has decided he really doesn't want to go. So we'll have respect for his body and not try taking him to time out, this will keep him from becoming aggressive about it. You can't expect him to not try his best at getting what he wants, that's what dogs do, yours just does it through growling.
So don't bring him to time out, get up and turn your back, completely ignoring the dog. If he pulls at pant legs then leave the room instead or quickly loop his leash to a stationary object so that he cannot get to you while you stand on the other side of the room ignoring him completely. This way he learns that his method of playing doesn't seem to be working. You still must teach him the right way to play though.
after 30 seconds to a minute (so long as he has stopped trying to get you to come back) go back and pay attentions but remember he is likely in the same mood as before (playful and rambunctious) nothing has changed that. So set him up for success by immediately engaging him in play with a toy. Try all sorts of toys. You can make a small flirt pole (a stick, thin rope and a stuffed animal toy-basically a large cat toy) and use that is he really like to chase. or play tug with a large enough tug toy that he won't accidentally get you instead of the toy.
As for the growling when he's being "disciplined", from what you described it is a normal dog trying to avoid unpleasantness (getting valuable things stolen from him, getting punishment). so the first thing to change is the amount of punishment. Try not to give so much by setting the dog up for success. any punishment you do give should not be confrontational such as yelling, scruffing, alpha rolling, dragging into time out, hitting, pinching, grabbing, popping the collar, jabbing the dog with your fingers, etc. All these things will make the dog feel he needs to defend himself from you. from what you have said so far, if you do not stop threatening your dog (just because you don't think it's a threat does not mean the dog agrees) he will not stop trying to defend himself from you, I fear he may become aggressive when you push him too far. Some dogs just go to their happy place and try to make the punishment end as fast as possible, some dogs tell you that they have had enough.
So stick to punishment that looses him things. He bites he looses the fun game, he jumps up he looses attention, he pulls on the leash the walk stops, etc. and also focus on prevention. Teach commands that can be used for fixing bad behaviors (dogs can't jump up if he's sitting, can't bark at the dog is he's staring at your face, can't eat the garbage if you tell him to "leave it", etc.). Also use blocking to teach him that some things don't work. If every single time he tries to steal something from the table you step in front of him and don't let him get to it (don't touch him, just block him) he'll eventually give up. This also involves prevention, if you are not there to work on training something he needs to be prevented from rehearsing the bad behaviors. use crates, gates, leashes and doors to restrict his access. A leash on all the time when you are home will also help to prevent the biting. You are quickly able to remove him from whoever he is biting and can prevent him from getting to the people he wants to use as toys.
It's also important that he succeeds as much as possible. That gives you more things to reward, and trust me you'll need to use something better than "good boy" and some petting. Use food, yummy food. Carry it around in a fanny pack or something similar so you are always able to quickly reward behavior you like. Too often we forget to notice the dog when he's doing what we want (like picking up a toy instead of grabbing a hand). In the case of playing with toys you may want to reward him by playing with the dog using the toy as treats may distract him, but only do this is he actually enjoys playing with you using the toy.
As for the "dominant" behaviors you describe, that's all bull poopy. Dogs don't walk through doorways in front of people because of status, what dog would have an instinct involving a doorway anyways? They walk through doorways because they are excited to got through and are faster than you. They pull on the lead because they are faster than you, they stand in your lap because they want to be near you, he growls during punishment because he doesn't like punishment and he feels growling might make it stop (if that doesn't work he'll try something else, maybe biting, maybe not), He is not a wolf, eating after you means nothing to him except that he might really want to steal your food cause he's hungry and sees yummy stuff on the table, when a dog sees food a dog eats food. None of this is dominance, it's logic. so stop trying to assert dominance and just try to teach the dog to do certain things. You can train your dog anything he's physically capable of, so use that. If he's doing something you don't like try to train him things to do instead that prevent him from doing the unwanted behavior (like teaching a dog who wants to attack other dogs to look at their owners whenever they see another dog, they can't kill the dog if they have to watch their owner).
I agree with no longer taking things from your dog. Think about it. Whatever the dog has is awesome, you walk up and steal it which makes him really sad. dogs don't like being sad so he wants to make sure he doesn't feel sad again. Next time you come near his toy he needs to do something to keep himself from getting sad, at first he may stare at you, cover the object with his head, run away, etc. all very clear messages that he'd like if you would not make him sad again. You don't listen and grab the fun things again and he is sad...again. so he has to be more obvious, you are obviously a stupid creature who just doesn't understand him so he makes his displays more obvious in hopes that you'll be able to understand him this time. This is when growling and snapping occur. you missed the more subtle request that you go away so he revs it up. Next step is often really biting. He doesn't understand why you just won't listen. I mean, why should he loose this awesome thing, he has no idea that it could be dangerous. So every time you ignore him and take things from him you are going to make him feel a need to get more forceful with his requests that you go away. so instead teach him it's fun to give you things (using food rewards and returning the object over and over until he stops worrying about it, after all you are going to give him something more awesome and just give the original awesome thing back) and also teach him it's okay if you are near his things. For instance walk up to him while he eats and add some of the meat from your dinner.
So just remember to predict, prevent and if necessary respond in a non-confrontational way that tells him this method of playing just isn't gonna get you what you want (a fun game). I would also start desensitizing him to things he might be uncomfortable with, like leading him by his collar, brushing, checking teeth, ears and eyes, or being lifted up. Do these things periodically through EVERY day and if he already dislikes them give him a treat afterwards. Perhaps he gets carried to the food bowl every night or gets his teeth brushed before every walk. life rewards like that work well for these things, they create a positive association, the dog welcomes the uncomfortable thing because it means the fun thing is gonna happen soon. make sure this dog gets loads of socialization (playing with other dogs, meeting leashed dogs, meeting TONS of people of all ages and going to TONS of different places with different noises) so he does not find many things threatening.
So I hope this helps, sorry it's so long
