Kitten w/diarrhea and blood

Question
I have a 6 mo old kitten I adopted from the shelter.  He's been in our home since late July. We also have a 4yr old and a 1.5yr old cat (no dogs, yet). At that time I put him in the master bathroom with his kitten food and a catbox for several days until I was sure the other cats would not beat him up.  He had no accidents.  He was released full time after about 5 days, the box was left there for a while longer. We have three boxes in the house, one on each floor (we don't yet let him in the basement though). They are the huge rubbermaid boxes with a cut out on the side.  I clean them 2-3 times a week.  He does use them to pee all the time.  However he started pooping in the bathtub of the master bath about a week after I removed that catbox.  It was diarrhea without blood. We shut the door and within 2-3 days he went to the upstairs bathtub.  That's when we noticed the blood, small amount of fresh red blood.  
I called the vet who thought there was nothing the matter and just suggested blocking off the area.  It has worked fairly well, but whenever we forget to shut the door, he poops in the tub. I filled the tub with 1-2 inches of water, and he just pooped on the rim.  Today, he pooped on the carpet outside the bathroom.
OK, the bathtub is irritating enough, the carpet is a whole other matter.  Its still bloody and true diarrhea, looks like a flat disk.
The vet gave him a wormer when I took him in for his post adoption checkup after 10 days.  In mid September She gave me Fortiflora to give to him to try to stop the diarrhea.  I got three packets (days) into him before he got some impaction and threw up for 2 days (he has a penchant for my daughter's hairties).  He's eating normally and acting normally now.  She also gave me a liquid wormer, 1/2 immediately and 1/2 after 3 weeks.  I failed to give it immediately and then waited because of the impaction, but he's since gotten it.
I am at my wits end with this.  I'm sorry this is long, but my vets only suggestion is to put the catbox into the bathtub (no way).  I did put a little one back into the master bath - I don't want it there permanently due to space.
any suggestions are appreciated.

Answer
My first questions to you are these: Has this kitten been checked for protozoan infections such as coccidia, giardia or Trichomoniasis?
What are you feeding him?
Kittens as well as cats stop using the litter box when they are trying to tell you something. This cat is telling you that either the food is upsetting his digestive tract or he has an infection that isn't being caught.
The fact that the other cats haven't gotten diarrhea means that he probably doesn't have a protozoan infection as they are highly contagious among cats.  But being older they also may be more immune. Since this cat was in a shelter he could have any number of infections, including leukemia. Was he tested for that? or FIV or FIP?

In the case of the food, if you are feeding something like Purina Kitten Chow he will have terrible diarrhea because it is coated with cow's milk and all cats are lactose intolerant once they are weaned.
So if that is the case, get him off of the Chow and onto Science Diet Kitten Growth so that he will have optimal nutrition and no diarrhea. Do it slowly over seven days then throw the kitten chow to the birds.

The blood is from the constant irritation to his little colon. Once the diarrhea is cleared up the blood will stop.
You can start adding a small amount of boiled rice to his food while you are working on the stool problem. Make sure you take a fresh sample to the vet to have it checked for the above infections.
If you cannot get it there fresh, wrap it in plastic and stick it in the fridge. I know it's gross but it's the only way to keep any eggs in there from hatching so that they can be identified.

I think once you clear up the diarrhea his potty habits will also revert back to normal.
I hope he gets well soon. Please let me know what you find out and how he does.