It would be a miracle if he were housebroken by 17 weeks

Pups of that age just aren't capable of full understanding of the concept of housetraining. Which you can see pretty clearly in the fact that he's wetting his crate at night. And
would see during the daytime if you didn't predict and provide for his needs well.
You must be a good manager of his needs during the daytime if you're accident free then

You just need to manage his night-time needs equally well, and you'll be accident free then too.
One thing I'd note at the outset is that the problem probably stems from the fact that he's waking up - which in turn is probably because he's in his crate alone. I'm not suggesting you change that, but rather aiming to give you an idea of why it's happening so that you can better manage things. Thing is, like all mammals (you and I included), when the pup is deeply asleep his non-essential bodily functions like urine production will slow down (instead the body concentrates on growth and repair). That's how come we can all happily sleep for 8+ hours without having to get up to empty our bladders - but we wouldn't have a hope of lasting that long during the day (or at least, not without severe discomfort). Anyway, that all works fine until we actually wake - upon which, emptying the bladder is a matter of some urgency (especially if you're a baby with only a little bladder).
Now, he probably slept right through when he was in bed with you because he was nice and safe and warm and secure. Now he's on his own and not so safe and secure. So, he sleeps less deeply, and hence wakes up. Having woken, he must empty his bladder. And so, he wets his crate then cries.
Chances are, he'll eventually start sleeping through the night on his own as he gets used to being on his own. But if he's wetting his crate in the meantime, then there's a risk that he'll get very used to it and lose inhibition about doing it. Plus, you've got to get up to a wet crying puppy. I would thus suggest a couple of things. First one is to set yourself an alarm to get him up and take him out at 2am (or whenever is the earliest that he cries). If you're going to have to get up anyway, it might as well be because of an alarm as a screaming pup

And if it's you waking him, you will probably avoid the wet bed. So, you take him out, let him empty his bladder, then put him straight back to bed.
This doesn't go on forever, of course. You should gradually start pushing back the time of the alarm until you reach morning and he's sleeping through again. It probably won't take more than a week or two at his age, because his bladder is big enough to make it, he just needs to settle enough in the crate on his own to sleep deeply enough not to wake at night.
And the last suggestion is to give him a worn teeshirt or something else with your scent on it that he can cuddle into at night. Once again, it's aimed at helping him to settle enough on his own to sleep deeply and not wake part way through.