Skaff offers twin homes and single family. http://www.skaffapartments.com/
Candlepark Properties are town homes that allow pets. http://www.candleparkproperties.com/
I'd suggest continuing to look for rentals in North Dakota. Just looking on Craigslist, I found a lot of homes for rent in Fargo. I searched for 4 or more bedrooms. They appear, generally, to be going for $1,100-$1,400 a month. See http://fargo.craigslist.org/search/apa?query=&srchType=A
I'm not crazy about Craigslist, though. My first suggestion would be to contact a Realtor in Fargo to help you. But the point is: There appear to be plenty of rentals available.
Hope that helps.
Do you have any funds available to bring to closing in the event that you are really close? This might be another option to help you avoid short sale. And I personally do not know of any bank that is going to give you a home loan immediately following a short sale. You might want to get connected to a property management company in ND to help you locate a place to stay in the interim.