Cat Peeing

I have a cat named Loki that is a mess.  About 50% of the time, he's a normal cat.  He will sit with me, and purr and appear content and use the litter box.  He also normally has a really good appetite.  The rest of the time, he eats toilet paper (clean) and any other paper product he can get his mouth on, pees on the carpet, and bullies one of my other cats.  I want to detail exactly what he has to deal with on a daily basis because I would really like a good idea of what my options are with him.  

Loki is a male cat and he is about a year old.  He was rescued after being separated from his mother probably too early.  The behavior that he exhibits which I find odd is as follows:  He eats paper products, and loves toilet paper.  He pees on certain spots on the carpet and on very specifically textured rugs (bath mats, and sometimes dog beds.)  He will sleep with and cuddle up with one of my dogs and one of my cats, but will bully the other, older cat. He chews wires.  About 3 months ago, my MIL came to visit and brought another dog with her.  Loki was so stressed out that he stopped eating and almost died from hepadic lipidosis.  He made a fast recovery after MIL left and started eating everything in the house again.  He will also knead and suck on anything fleece, particularly blankets.
 
Loki lives in a 2400 square foot house with a 7 year old female cat, a 2 year old female cat (he was rescued with her) a 6 year old female lab mix, a 2 year old male husky mix, my wife, and myself.  All animals in my house, including Loki, are fixed.  He eats raw chicken necks, backs, hearts, and gizzards in addition to several supplements (about 3.5oz a day).  He shares three litter boxes with the other cats.  My wife and I have put up a 6 or 7 foot cat tree with several places for him to feel high up and hide.  There are toys and things for him to play with all over the house.  

Since the peeing is really the major issue, I will detail what my wife and I have done to attempt to fix this.  We bought and placed 4 Felaway pheromone diffusers in our home.  We have bought and frequently employ enzymatic, pet specific carpet cleaners.  When he pees on something, he is placed in the location of a litter box and usually locked up with the box, water, and food for a few days.  (I have read that this is a way to break a cat of peeing on things...not working).  Nothing we have done has made even the slightest change in his behavior.  We are both at our wits end.  

I'm not sure what else I should say about Loki, other than that I am willing to try anything to get him to stop peeing on things.  If that means giving him to a family with fewer or no pets, then so be it.  I don't want to take him to the pound or a rescue, but I'm moving soon and I will not own the house I live in when I do, so I cannot have him peeing on someone else's rugs.  I really need some help with this if anyone has any to offer.

The first thing I would do is get him to the vet.  Be sure he doesn't have a UTI. 

As far as the paper eating, I would keep all bathroom doors closed.  My guess is that the paper is entertaining to him.  One of my cats loves to unroll the tp and then takes pieces of it and sometimes eats them.  He also loves balled up pieces of paper.

This same cat also would pee on certain textures.  We had a vinyl type bean bag chair that he peed in over and over again.  We also had a parachute material of a cat tree.  He did the same thing.  It was just the material that attracted him .  We just got rid of it all and the peeing stopped.

As far as litter, have you tried Dr. Elsey's Litter Attract?  It works well to attract cats to the litter box.  Also are the boxes all cleaned daily?  What type of litter boxes are you using?

Here is an article on Litter boxes and two videos that might help you out. 

http://www.thecatsite.com/a/litterbox-problems-in-cats-the-ultimate-guide