We have a year old kitten, he has been spayed, and after the last trip to the vets, we were told he is fit and well.
We have always had a problem with his litter box/training etc. when we got him we were told he was litter trained, we got him when he was 12 weeks old and he settled in well.
Long story short, at first he refused to go in his tray at all, if he was outside he would hold himself until he got in the house then he would pee all over the floor. Never even NEAR his tray.
We tried a few different brands of litter and he was never happy with any of them. Somebody suggested using compost and it worked!
He has been using the tray for a few months now. The only thing is this.
We will come down in the morning and everything he did in the tray will be all over the floor, he tends to throw everything out of it.
It has gotten to the point now where we are finding bits of compost and waste on the OTHER side of the room, a long way away from the tray.
It is always kept clean,and we haven't changed our cleaning products etc.
We just want to come down one morning and not have to brush the entire floor all the time, we put paper under the tray but it does no good.

Do you have a covered litter box with a flap he has to go through? That might do it. Also, face the opening of the box towards a wall-just leave enough room for him to get in and out. You'll have to put him in it when you get it set up to show him what it is.
Good luck-sounds like you've got a spirited fellow!

Also when you do that, try to put a piece or two of his mess in the box after you change the litter. If he smells it, it may encourage him to go in there.