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Under the federal law, the Manguson Moss Warranty Act, they are bound to honor the exact terms of the warranty. If they are not honoring those terms, which is what you are stating, they are in breach of the warranty. Under the MMWA, you have a right to first file a complaint with the FL Attorney General Consumer Protection Unit for them violating the MMWA and not honoring the warranty. In most cases the AG can resolve these claims, but if they cannot, you have grounds to sue the company for breach of warranty and all costs and expenses you incurred from their breach.
The company has a nerve telling you that if you went elsewhere for work that it would void the warranty, because as you are saying they are making you pay for everything, so what warranty is there that it would void.
You need to contact the AG and if they do not settle this, then you need to get a local consumer protection attorney and sue under breach of warranty and violation of the MMWA, as well as unfair and deceptive practices, which can allow you to seek punitive damages up to three times your actual damages plus attorney's fees.