Puh rabbit is a tough one. Mine can have duck, luckily, which is easier to find, although I now feed a wet food and add fresh. It may be the only option for you in the end. Is it only the meats that he reacts too? Mine has many intolerances and I found that with any dried food I would end up getting issues because there would be stuff in it that was not supposed to be in and/or he may have been reacting to the preservatives too.
You may want to consider trying to find 100% meat tins (I feed "Hermanns", which is a German brand, not sure if they have rabbit only tins) and then add your own veggies/carbs. It is easier than homecooking as you do not have to cook any meat and the tins include bones, etc. Just need to do some calculations to try and balance it and/or feed a variety as much as possible. You can also try and find someone more experienced to help you.