Does the rental place you will be living in have a no pet policy, or a limit to pets, or exclude specific pets? Sometimes that can be negotiated, especially if you put down a pet deposit. I know that you have spoken with your vet, but do they allow people to post animals needing a new home in their office? That would be safer than posting them on FB or Craigslist.
Do you have any relatives or friends who could keep your rabbits while your home is being built? Since your rabbits are bonded, they should remain together. Not many people would want to adopt 3 rabbits at once, and I would be wary of posting on FB or Craigslist anyway.
Rabbit rescues are often full, and sometimes don’t get back to people. I would keep trying them, and you may have to contact rescues further away from you. Here is a list of rescues by state, if you are in the U.S. I don’t think it’s entirely up to date, some may have closed, and there may be new ones not listed, but it might be helpful. http://rabbit.org/independent-rabbit-rescue/