Preventing kitten biting people?

I have a 7 week old "foster" kitten (rescued feral at 5-6 weeks old.) He stays in a large cage when I can't keep an eye on him because I don't have a safe place for him where he can't get into mischief if there is no on watching, and he is only allowed loose in the bedroom because he has to be kept separate from my cat...
The first 1-2 weeks, he was very loving and cuddly, and only played with his toys. Now he is getting more wild and when he is loose in the bedroom or up on my computer desk he will leap up and attack (in play) a person's body parts! He plays very rough! If you reach down to pet him or pick him up, he will try to nip and bite your hands. Not because he doesn't want petting or to be picked up--as soon as you lift him up he will start to purr-- but just because he wants to play with everything including hands!

I really don't want him to learn that biting is acceptable behavior but I just don't know what to do to stop it. I tried giving him a toy to bite instead if he goes for the hands, but this does not seem to discourage him from trying to bite human hands or whatever else is within reach! I really want to discourage this behavior now while he is still young...

Tell him no, hiss or make a "pssst" noise. Remove your hand (or whatever he's attached to) from his mouth slowly, moving fast only riles him up more and will make him think you want to play that way.

Get some wand toys and sturdy balls he can bat around. Start letting him out for as much as you can -he probably sees that now as a sort of 'on' switch and goes into spastic play mode, hence tackling you.
It's good that he is choosing to interact so boldly after such a short period of time.

Any chance that you'll be keeping him, or getting him vet checked/tested so he can possibly be out more and maybe hang out with your other cat? If your cat permits, it could really help teach some kitty manners.

Oh, and kitten proof to help keep him out of trouble.

There is a very slight chance I might be able to keep him, but probably not. I also don't think my cat will accept him, she is very unhappy about him being here...
He has a cold or influenza. He has been tested for FIV/FeLV (this week actually) and wormed once, but the vet said it takes 2-3 treatments to get rid of all the worms and that he should be retested for FIV/FeLV in 3 months because it is possible to get a false negative, so I also don't want to possibly expose my cat to parasites or diseases. The vet said he can't be vaccinated until he is healthy from whatever cold/flu thing he has.

Try taking advantage of his inherent prey drive. Get some very small cat toys (i.e. those small fuzzy mice that come in packs) and keep one in your pocket. When he attacks you, catch his eye with it and toss it. He should immediately let go of you and chase after it. I raised a feral kitten and used to use this method all the time - she seemed to learn very fast that toys could be much more fun than human body parts.