Are you sure it's the cat - i.e., have you had allergy tests done? If this is an indoor/outdoor cat and you're just noticing a reaction, it could well be the pollen on the cat's coat - right now we are at the peak of Ragweed season - if that cat is wandering thru fields of ragweed, then he's sure to bring that home. We have lots of allergies in my family - just not to cats (we have all been tested by an allergist). But, to minimize the exposure to the dust and other stuff that cats drag around, we keep them out of the bedroom - that's the most important space to keep clean if you have allergies. Also, a HEPA air filter (which makes a great white noise machine) would help tremendously in her bedroom, as well as having one in the living area. Cat allergies without other allergies is actually quite unusual - common house dust (that hosts a wide variety of potential allergens) is often the source of many allergic reactions. We also make sure that any item the cat spends alot of time on is washable.
It sounds like you've provided a wonderful home for this cat and honestly from what you say, I doubt he would ever warm up to anyone else, so I would encourage you to do everything you can to keep him. One option would be to buy a dog kennel (with a nice covered house) that you could keep him in at nite or give him space in the garage or even a backyard shed. With his personality it is highly unlikely that he would be adopted - there are just too many other cats that would be chosen over him. I'm a cat person and if I would not consider adopting him (and I've had my share of problem cats over the years), I honestly think it would be very difficult to find him a home. Even if someone were to take him, do you really think they'd love him and care for him as well as you have?
I will pray that you will make the right decision for the cat.