The IRS only lists three acceptable methods of determining your mortgage principal in most circumstances: the average of first and last months, the interest rate method, or the average of the monthly statements provided by your lender. While your method of using an average daily balance seems perfectly reasonable to me, it is not specifically included as one of the IRS's acceptable methods.
Since you are so close to the cusp, you can check your lender's statements for the month of purchase and the month of sale to see if they report using the average daily balance.
@seattlelostpack
