Is it permissible to conclude a car sale contract in this manner, and is accelerated payment of the remaining installments sufficient to eliminate any doubt if it exists, and would the car then become permissible? And can the company change the contract to be between two parties?

This transaction is usurious and impermissible, because the third party paid the price on your behalf to collect it from you with an usurious increase. We hope you have an excuse for your ignorance of the true nature of the matter. Hasten to pay if that absolves you of the usurious interest.