Since the city is willing to work w/you on fixing the foundation, why don't you spring for the cost to have a Structural Engineer do an assessment of the foundation? For a few 100 $$$s, I would think that it would be CHEAP as far as any cost to you to have your foundation fixed. Worst case - If the city doesn't fix it, you'll know EXACTLY where the house 'sits'.
My best to ya and hope this helps.
PS: If you have any other concerns about the overall condition of the home, I'd consider hiring a Home Inspector that has 'contacts' with experts such as Structural Engineers, and the like.