The short answer to the question "do auto shipping payment plans exist" is no. Most auto transport companies require payment in full when it is due. Luckily, most shipments cost under a thousand dollars, and payments are typically split between a down payment and cash on delivery.
Brokers typically charge for their services either at booking or at dispatch, while carriers take their payment on delivery. While many companies are happy to work with you in terms of how you pay and when you pay, payment in full will be required and payment plans for auto transport usually do not exist.