Yeah, its gonna be tough no matter what. Its not just that you have dogs, its the number and the size. You can sometimes use a big deposit as a bribe. Also, when we rented with dogs (smaller and fewer though) we made sure to say "We have 3 small Crate-trained' dogs. They only come out to potty or eat or play, they do not get free roaming privieleges". Sometimes the fact the dogs will be crated will help sway an undecided owner.
I dont know how the real estate market is in your area, but if its anyhting like my market, you may have plenty of time to find the right place.
I hope you guys are able to sell quickly and find the perfect place soon!