Bought 2 vehicles in SC from 2 different dealers about 3 years ago. Procedure I used was to:
Before you do anything, Make arrangements with your mail service to handle the title/transfer with the SD DMV. You will have to give the mail service a very limited power of attorney to handle the transaction. They can also tell you how much you will owe SD within a couple of dollars.
Tell the SC dealership up front that you are registering the vehicle in SD and will not be paying any registration fees to SC.
Send all required paperwork to the mail service along with appropriate amount of money and then wait for the plates to come.
SC should give you a 30 day temp plate. Pay attention to the expiration date, one dealership was very slow (lazy) with completing their end of the paperwork, so they had to give us the 2nd temp plate at their cost.
Good luck, safe travels