I am thinking about entering the dividend payments as as they were paid directly to me (passed through) but not sure if there is anything else I need to do.
Since the IRS considers a single member LLC as a disregarded entity, it doesn't matter if the EIN or your SSN is on the tax reporting document. You enter any tax reporting documents exactly as printed. Since the IRS issues the EIN, they already know exactly what SSN that EIN is tied to. So enter your 1099-DIV under the personal income tab in the Interest and Dividends income section.