Why worry so much? For most people if you need to go to nursing home for long term care. You are never going to have enough money to pay for that. Best way to do it is to give all your money to your children (3 yeare before you need to go to nursing home ), then , let govement pay for your nursing home bill.
For most people, if you pay off your home, your property tax is not very higher, SS should be enough for living.