Unfortunately, unless you have a signed contract or can demonstrate other express agreement to the terms you wish to enforce (e.g. oral committment), there is no legal grounds for you to assert that the comply with those contractual terms. Paying the invoices does not commit them to terms other than those presented in the invoice.
I wish I could give you more ammunition, but you would just be sending good money after bad.
Please let me know, if you have follow-up questions.
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