with all due respect, getting a professional involved and paying them is probably more than the will be saved in taxes than by just following TT's questions and responding appropriately.
there is no dispute that the NC tax forms are be completed first.
Whatever is paid to NC becomes a credit to SC.
if your joint income is in the mid $30,000 range, all the tax will be paid to NC and close to nothing will be paid to SC in any event - regardless of how many months you lived in SC in 2019. Above that figure SC marginal rate is higher than the NC marginal rate, so something will be due to SC.
