The interest paid divided by the interest method in Pub 936 applies to mortgages held throughout the year. With that said, this method, and everything else in Pub 936, does not make sense when you sell your existing main home and purchase a new one in the same year. This method when applied to a mortgage held less than 12 months, approximates the 12 month average with $0 balance inserted for months the mortgage was not held.
The IRS concluded in memorandum [removed] (2012) concluded that tax payers could use any reasonable method to determine the amount of deductible interest. I don't know how relevant the memo is today, but we all know Pub 936 is not reasonable in the case of selling and buying a main home in the same year.
You can only have one main home at a time during the year. I think it is reasonable to treat your sold and bought homes as one aggregate main home. Both the 'interest paid divided by the interest rate' and the '12 month average' averaging methods will work for this. In order to be really reasonable, you should replace the interest and balance for one of the mortgages with $0 in the months the two mortgages overlap.
