"My previous lender actually applied $164,666.95 towards the remaining principal, and $754.72 towards interest."
So the total amount applied to the existing mortgage before the refi was $165,421.67. That's the same exact amount of the new loan that is applied to the residence also. Therefore, you will be able to deduct 81.3% of the interest on the new loan, since 81.3% of what you borrowed on the refi is to pay for the house. The remaining 18.7% was used to pay unsecured debt on which the interest on that unsecured debt is not deductible.