I'm so so sorry that you find yourself in this absolutely terrible situation that you never expected to be in. If there is one of your rabbits that you are finding especially hard to have to let go, then I am happy to in effect foster that bunny for you, and neuter, vaccinate, and then when ypur luck changes which it will do, then you can look forward to having your bunny back.
Maybe you won't feel quite so sad then, if you can still actually keep one, but you need time to sort out things in your life.
You may well find that when you have been in your new place a few months, and have proved yourself a good tenant, that they may well agree to you having a rabbit then. This is what happened to myself in the past, and actually when I approached the letting agent, they did clarify that the 'no pets' clause in general applies to cats and dogs, and the biggest concern is usually dogs left barking everyday, but my then landlord was perfectly ok with my then rabbit.
Have you actually asked about keeping a rabbit, or are you reading a 'no pets' clause as absolutely no pets, because that may well not be the case, especially if you will be working from home, and can guarantee that the rabbit will never be left loose whilst unattended.
It sounds like your buns have already suffered terribly, and I will definately help you out with one of them, and as I said if there is one you would love to have back one day, then I am happy to have that one for you. I would be very surprised if you couldn't have one at your new place in a few months, especially with you working from home.