The new legislation would not affect you at all if you rent out the house.  There's no cap on the mortgage for a rental property, which is what you would be converting your former primary home to.  The mortgage interest and other expenses related to the rental are taken on Schedule E and not as primary residence interest on Schedule A.  

Since you would be renting your new place, you would have essentially no home-related deductions on your Schedule A at all, except for the part of the year before you convert the house to a rental.  You may revert to taking the new higher standard deduction because, with little er no home-related deductions for Schedule A, you may not have enough to itemize.

You would not owe more tax if, as you say, the rental expenses cancel out the income.