There's no rule that says a birthday gift has to be a surprise. Why not just take them to the store on their birthday and let them pick out what they want, or let them pick it out beforehand and just tell them they can open it on their birthday. We changed our entire birthday attitude after five years of struggling. We don't have a party with young kids (older kids and adults only) and we don't do gifts. My son doesn't care one bit that he isn't getting a gift. We make such a big deal over him for the entire day (hire someone to play guitar because he loves it, decorate the whole house with his favorite themes, etc.) It takes some trial and error, but I would assume siblings don't really like the meltdowns or anxiety, either, so they'll likely be happy to go along with whatever works for their brother.

we tried birthday parties for years but our autistic guy hates it! so we changed how we approach birthdays. so on each one of the kid's birthdays it's there day, they choose what they will do that day such as going to the zoo with just mom & dad & they get to do all the extras they don't get to do when we go as a family (4 kids not affordable to do extras for everyone) so we do there day, the child gets to buy his/her own present from the gift shop.
my suggestion would be let him in on the planning, buying the supplies, decorating, make it a special trip to the store to buy his present, then wrap it so he can still open it on his birthday.

My oldest has high anxiety and little patience too. He also has the last Birthday of the year (a December Birthday.) It is particularly hard on him since we have 1 Birthday in August and 5 Birthdays in Sept. So he has a long wait after much partying. The way we have gotten around this is we involve him in the preparation and planning in his siblings/cousins Birthdays and "pay" him for his services. He is then allowed to buy a gift of his choosing with his earnings (his earning depend on the amount of his involvement.) As far as patience to see what he gets for his Birthday we involve him in that too. He is brought shopping for his own gift but is not allowed to have it until his Birthday. We start by him making a list of items he wants. Then we bring him to the store to price his wants. He is not allowed to buy during this stage. We tell him how much he is willing to spend and he prioritizes his list accordingly. My son isn't really a big ticket winner type of child but he enjoys getting the most for his money. He actually enjoys rearranging his list to see which way is the best. Finally as it gets closer to his Birthday we allow him to make his purchase. Only our gift is done this way and all other gifts are a surprise. He has done very well with doing it this way.