Oh man, I am so bummed to hear about your situation! We are in the SAME boat! I think our LL has given us a few extra months or weeks from his original May 1st deadline, but I'm not positive. Such a HARD, hard place to be.
We are in Auburn, so not far from you! Definately look at the Sacramento CL ads and on the righthand side of the CL homepage for Sacramento, click on "GoldCountry", there are ALOT of very pet friendly properties at very decent prices and they get good internet too! You may have to go out a bit, like Grass Valley, Pen Valley, Lake Of the Pines, or even a bit further, but its not too too horrible, maybe a 45 min drive to the nearest super 
walmart, but many of those towns have great shopping and sevices, and Auburn isnt too far away and we have a few major stores and feed stores and several grocery stores.
I really hope you find something that will suit you all. I am still trying to adjust to the idea of not having my chickens when we move  
   I dont think I will find anything with 4+ bedrooms, 2+ baths, 2400+ sq feet that will allow all our animals (dogs, cats, rabbits, horses,and chickens) and fit our family needs and budget. We are just not ready or able to buy yet and we HAVE to stay in or very near Auburn. I think we are going to have to say goodbye to most of the extra critters, and board the horses. Of course we are keeping the dogs and outside cats, but I think thats about it for us.
I think you may have a very good shot at finding a place out in the areas I suggested, many people will work with you $ wise, and you may be able to get in in time to still plant a new garden AND keep your flock. Those places are decently rural and there are alot of folks with far more animals than just chickens. I really, really, hope you can find the right place to meet all your needs and wants.