Please help. Male 9 month old cat pooping outside the litter box

I got him as a rescue when he was 4 months old. At first Jupiter would use the litter box with no problem. We went to the vet to have him neutered,per humane society's policy,and after he still used the litter box to poop in. The vet said he had crystals around his penis, and ordered us to feed him Diamond brand indoor cat food. For a while after changing the food he was okay, but about a month later he started pooping outside the litter box. We took him to a different vet to have him checked out, and the vet just put him on some medication for a cold he had. He is currently finished with his medication, and is no longer sick.
We have 3 cats and 1 dog. His brother and sister are older than him, but very nice regardless. The dog and him play whenever Jupiter initiates it, and we took great care to provide a dog free zone for the cats.
We have two litter boxes, each with different litter because his sister prefers one kind and his brother another
He just got out of 'foster care' when we got him. All we know is that he was very sick for the first few months of his life, we don't know if there was any abuse
We love him very much. He is technically my cat and being he is the first cat of my own I baby him completely
He always poops RIGHT next to the litter box. It's never in the exact same spot, but it's always a couple inches away.
We took the lid off the litter box, just incase that was part of the issue
It's not a matter of being scared of the other animals, because he does this even when he is alone with me and my door is closed.
He uses the litter box to pee, but only poops in it once or twice a week. We be sure to give him a treat when we notice that he pooped in the litter box, hoping positive reinforcement would help; it has not.
He is not declawed, nor will he ever be.
We have cleaned the carpet various times with a carpet cleaner, that has also not helped.
I just don't know why he's doing this. According to the vet he's perfectly fine. I love him with my entire being, but it gets tiresome having to clean up, and it causes me to worry greatly about him and his wellbeing. I appreciate any and all suggestions. Thank you so much.

Try adding another litter box (even 2). You have 3 cats now and two boxes might not be satisfactory. 

Welcome to TCS! 

There's a lot that can be just a bit "off" with a litterbox and enough to make him do his business just outside of it. A history of medical issues that make him associate the box with pain can be one possible explanation. I agree with @yayi  that adding one box and even two can help. With three cats you need three boxes (preferably four) and it will also give him a choice of more boxes which hopefully will not be associated with pain.

More about litterbox avoidance and how to solve it -
[article="32366"]How To Solve Litterbox Problems In Cats The Ultimate Guide  [/article]

The idea of another litter box is good and might fix the issue (you should have one or more for every cat you own). You could also try changing litters completely. If your others are clumping, try a non clumping. You can even try the pellet stuff. If they're scented, try unscented. You could also try putting one in a different room. Maybe he hates the location. My parents' cat is afraid of the basement and they had to move the litter elsewhere.

It sounds like instinct makes him WANT to poop in the litter since he's going right next to it. This is weird to type...but maybe dust irritates his penis crystals or something.

When we adopted a 6-month-old Russian Blue kitten, he was kept in a large room, separate from the other two cats, because he was aggressive. He didn't like it one bit and showed it by constantly howling like a fire siren and eliminating right beside the litter pan. We finally took all three to a feline behaviorist to try to integrate them. She suggested a couple of things. One was that we change the litter to Dr. Elsey's Cat Attract. It's light-weight, dust-free, and strongly clumping. It has some herbs in it that attract cats. It keeps odor down almost completely. It works superbly in self-cleaning cat pans, much better than the recommended stuff which quickly destroys the pan. 

Darwin watched as my husband changed out the litter. Within just a few seconds, he was in the pan. He's never made a mistake again. The other cats like it also.We have four pans and it's all we use. One pan is in the bedroom and there's no odor. 

Cat Attract is available at PetSmart or Petco. It may be available at other places also. It's great for all cats, not just those who have litterbox problems.

You might also have your vet check the kitten. Sometimes they have a bad experience in the box such as pain urinating or defecating. That puts them off using the box. It's worth checking if the Cat Attract doesn't help.

When we adopted a 6-month-old Russian Blue kitten, he was kept in a large room, separate from the other two cats, because he was aggressive. He didn't like it one bit and showed it by constantly howling like a fire siren and eliminating right beside the litter pan. We finally took all three to a feline behaviorist to try to integrate them. She suggested a couple of things. One was that we change the litter to Dr. Elsey's Cat Attract. It's light-weight, dust-free, and strongly clumping. It has some herbs in it that attract cats. It keeps odor down almost completely. It works superbly in self-cleaning cat pans, much better than the recommended stuff which quickly destroys the pan. 

Darwin watched as my husband changed out the litter. Within just a few seconds, he was in the pan. He's never made a mistake again. The other cats like it also.We have four pans and it's all we use. One pan is in the bedroom and there's no odor. 

Cat Attract is available at PetSmart or Petco. It may be available at other places also. It's great for all cats, not just those who have litterbox problems.