Not trying to be nosy, but you may increase your odds if you include a little more information than just South CS, financial terms and lot size.
For example, by mentioning the zoning and south CS, that would indicate you have a preference for schools. So, which is it? Not every property owner pays close attention to that (especially if they are an out of town owner, etc) so if you have areas in south CS you prefer, you might list that.
Is there a minimum number of bedrooms?
Do you have a deadline (like prior to August when school starts for 2019 and the new zoning takes effect?)
You may also have some luck if you drive around looking at homes in southern neighborhoods with for lease signs up and call and see if any owners are willing to sell. I saw some over by Creekview elementary for example.