You’re going to need to let them to inspect the sofa. No retailer is going to give you a refund on a custom order just because you’ve told them it’s faulty. Whether the person inspecting your sofa on behalf of the store is employed by the store, by the manufacturer or an independent furniture assessor contracted by the store is irrelevant.
By refusing to allow them to inspect you’ve just been added to the “difficult customer pile” so can now expect very little proactive help from the store. If I were you I’d get straight back on the phone to the store and arrange for your sofa to be inspected.