One possibility of course is I can pay up the principal right after refinance to bring down the mortgage to the previous amount. A gimmick I may have to play.
Not sure what your train of thought is on that, but it's wrong. If you owe $250K on the current loan and you refi for $1M to cash out $750K, and you don't invest any of that $750K back into the rental property, that means you can only claim 25% of the interest you pay on the loan on the SCH E, for the entire life of the loan. Paying it down to "what you owe" won't make any difference.
At best, the remaining 75% of the interest paid would be an itemized deduction on SCH A subject to the SALT limitations.
