I did a mock return for South Carolina and found that the state tax addback was correct and that it did not create a line in the Other additions section. Possibly your strategy of starting over with your South Carolina return will work to get you to this point as well.
There are multiple items that can be added back and entered on line 1e. of the SC 1040. You can find the Instructions for SC 1040. Scroll down to Individual Income Tax packet for 2025 and open the PDF for instructions. The addback items start on page 24 of the instructions.
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