Sat down with a friend who's an accountant and tried to get them to explain how to do dividends and year-end closing for a company on the accounting side. As near as I can figure it, recording the dividends works like this:

Dividend Expense (the account I was missing) gets a ${DIVIDEND} expense, Dividend Liability gets a ${DIVIDEND} debit when the dividend is declared. Money (Bank Account) gets a ${DIVIDEND} debit and Dividend Liability gets a ${DIVIDEND} credit (balancing to 0) when the cheque is cut.

For closing it seems to work like this:

Balance Gross Income into Withheld Income, same with Gross Expenses (we didn't have Starting Equity this year). Now balance both of those to Starting Equity. At this point there should be 0's throughout the expense accounts as well as the income accounts.

Fun stuff.