If you have anything from your GC that specifies what "features" your home has, or what you specified, or anything that shows you were supposed to have heat pumps, then the answer is simple: lawyer up....that is the only thing that will get his attention.
In my state, this kind of issue could be called in to the construction industries board and they would send a state inspector out. These guys have the power to make things happen. Tennessee may have something similar....call your building inspector.
And I know you really don't want the expense, but get another reputable hvac contractor in to have a look. An independent, informed opinion will help you in knowing what course of action you can take.
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