The first thing you will need to do is look for the least dusty hay. Don't buy it from a pet store, go to a place where you can buy it by the bale and ask them for the one with the least dust.

Separate the bale outside and shake off as much of the dust as possible. Use a mask while separating. Don't store the hay inside if you can help it.

I know you have said you tried many different kinds of hay, but have you tried blue grass hay? Some people that are absolutely allergic to every other kind of hay have no issue with it, and it has helped many bunnies and guinea pigs stay in loving homes with people with allergies.

Some people are also great with Sweetmeadow brand hay (http://www.sweetmeadowfarm.com/products.html). It has practically no dust and the bunnies love it!

I have heard people swear by those air filters. They put them next to the bun's cage and it has even helped some people who were allergic to the actual bun.

I have also seen people cut a hole in a box or buy an enclosed hay feeder, so the hay won't get everywhere and is constantly enclosed with just a bunny head sized whole for your guy to eat through. You can cut a hole in the back of the enclosed litter pan as well, for even less exposure.

If you do end up needing to give you bun away, ask the shelters if you can foster. Remember, rabbit rescues want to help bunnies. If you give them a way to help you, they will! If you offer to get your bun fixed (not sure if he is neutered already, but it is a requirement of most reputable rescues before adoption) and to foster him until adopted, I am sure some rescue will be able to help. Other than that, try listing him on the classifieds section of Petfinder or posting fliers in your local pet stores (ones that don't already sell bunnies).

Just know that if you do decide to rehome, it will be a hard process. Not only is it harder to find a good quality home for a bun then say, a dog or cat, but your rabbit is also "plain." I know that you love his personality, but honestly, if someone were looking to adopt a bunny, and they could pick your sweet guy or a mean lop, they will pick the lop. I know it is ridiculous and sad, but I see it happen all the time. Looks almost always win out over personality. I fostered a boy that looked almost identical to yours. He had a winning personality, great litter box habits, didn't chew furniture, everything someone could want in a house rabbit. He ended up being with me for over a year, constantly being passed over for a bun with cute markings or a dwarf or one with blue eyes. That's just the way it is.

As for other people's comments, please don't just feed straw, it does not have the nutritional value they need. Don't feed just oat hay, it doesn't have the nutrients either, but will make your bun obese. Don't just use hay cubes, as rabbits need the long stems of the hay to wear down their teeth, and the cubes are just compressed little pieces (similar to particle board vs whole wood blanks).

Sorry for the long response, but I really think you have a great chance of keeping this bun!