Quick points:
In case it’s not obvious, the crate is NEVER a place of punishment. It’s simply too useful to you to be able to put the dog into the crate during certain times (technician coming over, moving out, etc.) to risk making it a negative experience for the dog.
Don’t hold a mouthy pup’s muzzle shut, or stick a finger down the throat, or rap the nose, or scold. You can teach it without punishment per se, exactly the way a puppy learns bite inhibition from littermates.
When the puppy bites, yelp or make a sharp noise of distress, then turn your back and walk away. 30 seconds or even less will be enough. Puppies learn from their siblings that biting means the other dog moves away and the play ends. You can gradually “calibrate” the bite force by reacting to gentler and gentler mouthing, until the dog is reluctant to mouth humans at all. As long as you (and other people in the household) are consistent with this response, it should work – and fast.
I was able to get a semi-feral pit bull puppy to learn solid bite inhibition in a few days – in fact, the dog started to learn immediately, I could almost see the smoke rising from her ears as she processed what had just happened. This is a potent technique. And because you’re not hurting the puppy, you’re not damaging the relationship you’re trying to build.
edit: Oh, and my rule for potty training is, “Am I comfortable? If so, it means it’s time to get up and take the dog out.” Also, it’s possible to housetrain positively – no nose rubbing or smacking. Just dip a paper towel in it, take the smelly towel outside, set it in the grass, and praise the dog. Show what to do, don’t punish for what came naturally.