Owner's dog is hyper and almost aggressive?

Yes, he does sound quite hyper! :-D Luckily, from what you describe, I don't think he's aggressive, just rather hazy on proper manners. I believe he would benefit from more exercise, if you have a way. Does he play fetch? Do you run? Do you have access to a bicycle with an attachment for dogs (Springer, or similar)?

He would also benefit from guidance and training. But this can be a tricky area; you shouldn't do training of a pet without the owner's permission. Also, the owner needs to be on-board and willing to do the training exercises between your visits.

The main remedy at the moment, besides physical activity, is distraction and ignoring. If he likes treats (and the owner okays it) try tossing a long-lasting treat away from you (behind him when you walk in the door, or off to the side when you let him out of the crate), then go about some business around the house.

If he jumps at you to play, cross your arms and turn away. I suspect he will come around to your front and continue pestering you, but just turn around again, and don't say anything. No pushing him away (that just adds to the fun of the "game" to him) and no saying, "No."

Most likely he will amp up the antics (like a young child saying, "Mom," then getting louder and louder the more she waves him off). The trick is to be more persistant than him. A time will come when the dog finally either gets bored or realizes his pestering isn't getting him anything. As soon as he calms down, praise him quietly :-D, or gently pet him. The key is low-key praise.

He will most likely need multiple sessions (and again, it's very dependant on the owner's actions between sits), but Labs are smart and want to please. He just doesn't know what is expected of him, and has too much energy to think straight.

Hope this helps! In the meantime, I suggest long pants, a long-sleeved shirt, and put your hair up in a bun :-D

I agree with Shannon - this isn't an aggressive dog, it's a dog that is not getting enough stimulation and hasn't been taught good manners. They're trying to manage his energy with the prong collar. The punishment he gets (prong collar tightening and putting uncomfortable pressure on his neck) for acting exuberantly may make him easier to manage on walks, but it isn't addressing the actual issue. He needs an outlet for his energy and he needs to be shown appropriate behavior rather than just punished for undesirable behavior. If you teach a dog what you want him to do, there's no confusion. If you teach a dog what you don't want him to do, he has literally every other option in the world to try instead, and he's unlikely to pick an acceptable choice on his second, third, fourth... try.

It's not really your position to train their dog, but at the same time I'd never advise against making your time with the dog easier. If you're using positive reinforcement methods, there's really no risk of adverse effects, and it doesn't really matter if the family is following your methods so long as you remain consistent. Even if he knows some basic obedience cues, it sounds like he's far too excited when you arrive to focus right at first, so simply asking him to do something like sit probably won't get you anywhere until he's dissipated some energy. Similar to Shannon's suggestion, I'd recommend distracting him when you arrive or let him out of his kennel to prevent his jumping. Treats might work, but for a dog who needs physical activity as much as he does, I would recommend trying a ball or a tug toy. Have the toy readily available and distract the dog with it so he focuses his attention on the toy rather than you. Immediately giving him something appropriate to do gives you something to reward - he's having fun and making the right choice. If he does redirect his energy onto you by jumping or mouthing the fun stops instantly. Become as boring as humanly possible. Be a tree. You can give a No-Reward Marker (like "no" or "ah ah!" or whatever) if you want - if you've used it consistently, the dog will come to associate the NRM as a cue to try a different behavior instead. As soon as all four feet are back on the floor and no part of you is in his mouth, the fun starts again. This way you can reinforce good outlets for his energy while establishing boundaries. Even if the family doesn't increase his stimulation and exercise, you can influence his behavior when you are present.