The math checks out. We're not really looking to change our overall mortgage payment amount. We plan on taking the amount we save and just adding that to principal each month. I don't want to be 72 when we pay off this house.
I believe the loan paperwork you sign states they have to be on the title and on the insurance policy as well. So if they are cool just holding the title in your name, go that route as it is easier for you.