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I do not have the 1120 software installed, but another tax professional sent me a screen shot of the screen in which you enter the start of business date (below). This screen is apparently 2 or 3 screens beyond the screen to enter the date of incorporation.

You are correct that the date of incorporation is not necessarily the start of business date; see the IRS discussion on this issue at §1.248-1 Election to amortize organizational expenditures paragraph (d) at IRS T.D. 9542.