Welcome to our forum! I'm going to give you my advice and you can take it or leave it. Since you've ruled out anything medically wrong with your kitty, then stress is probably the cause of the litter box issues. Know that cats truly prefer using a litter box as they are fasctitious creatures. I don't know how large your home is, but you might need to add a litter box -- one on each level may not be enough. Have you thought about the type of litter box or litter? He poos in the boxes but won't pee in them. Many cats prefer a box for pee and a box for poo, so please consider adding an additional box on the level he uses the most.
I would not even consider adding another cat to the mix until you get this situation resolved. You do not want to have TWO cats with this problem. My bengal was left alone for 9 hours a day while I worked full time and he was fine. There are many interactive toys you can get and the cat can occupy itself with them, but I don't know that this is the issue.
I would block off access to any area that he regularly uses. Close the doors to the room. Observe his behavior and if you think he is about to go, pick him up and put him in the litter box. If you have the time and patience, you can teach your cat to use your toilet.
It appears this has been an issue since the very beginning and once this habit starts, it becomes very difficult to change it. Since this happens more often after you are gone for periods of time, it could be separation anxiety. Bengals bond very closely with their owners. And it is not uncommon for a bengal to act out upon the owner's return.
Although medications may not be working, you might want to see if Jackson Galaxy's Spirit Essences has a formula for your situation.
http://www.spiritessences.com.
Most of all, do not yell or punish your kitty. He will not understand. He's doing something that comes naturally for him. It is not right that you need to cover furniture, close off rooms, and spend your time cleaning up the mess.
They do make diapers for cats. I think that would be a last resort, but they could help. Know, too, that there are portable enclosures available that will allow your kitty to enjoy the outside world. It's easy to train a bengal to walk on a harness and leash. However ... once a cat tastes the outside life, that's the life they want to have. My bengal has a huge outdoor enclosure on our deck and gets two walks a day. He has never had an accident outside his litter box.
Re-homing is always a last resort. You don't mention how the cat interacts with your boyfriend. Is he a cat lover or does he ignore the cat? There obviously IS a problem somewhere because this is not normal behavior for a cat. However, since it has been happening for so long, it may be impossible to stop it.