John,
Not sure of the municipality, but as noted by others the theory of using a monolithic pour vs footing, block and slab is not one of better vs worse, just another way to get the same result.
Not sure of your contract, and I don't want to know the details, but its simple to rectify in theory, contractor was contracted to either build the plans or an equivalent building. Thus X wide, y deep and z high. This is the grey area, does your contract say they need to deliver a building per plans and meet all the code requirements, don't answer that not for us to know. But at a minimum any reasonable person would be expecting a building to be delivered per code since a building permit and inspections are required for the project.
Another wrinkle, who got the permits? you or the contractor? again don't answer that, if you did, then the contractor is a sub and delivering a compliant building falls on you not the sub in that your dispute becomes one between you and them nothing else, vs reporting them to a system that will do nothing about the license.
If they pulled the permit, then ask your legal counsel how to demand that the contractor correct all the code violations on their dime and deliver the building with a certificate of occupancy, per state law.
Depending on the county you live in, you could file a compliant with the DCA and they will review the contract and talk to the contractor about the issue, sometimes it helps and sometimes its the norm for the contractor.
The flip side to this might also be one that you are over looking, not saying it is, but the contractor might have never intended to do anything wrong, but truly was trying to deliver the least costing option for you, and at the same time learning the method and process and just missed the boat on delivery and is now put between a rock and a hard place.
In either case you are left with the building as is now, what is the path of simplest correction and least cost and aggravation.
My father used to say, never shop price, shop the project you want and the product you expect to get in the end, get more than 3 estimates, listen to the references and then decide if I can afford what I want. In the end it is rarely ever delivered by the low-end estimates or even the high-end estimates, its delivered by choosing the right firm to build it and the cost is the cost.