It sounds like you definitely need to look at where $420 in heating to only go as high as 70*F is going. Granted I have a small (1200 sq ft) house in the South, but I don't pay anywhere near that and I'm setting the temperature wherever I feel like it. I'll sometimes switch between heat and ac multiple times a day. I generally keep the temperature between 69-74*F.
My system is a gas/electric "packaged unit" that sits entirely outside the house. It's a common retrofit to houses like mine in the Southeast because it's cheaper than finding room for/putting ducts in for a modern split unit (house had AC originally, but not a good space for modern split setup). Even with 60 year old doors and windows I never pay more than about $200 a month keeping my house as comfortable as I want it, usually much less.
Most of the time the heat is turned off. My apartment stays at about 72deg all the time, summer, winter, day or night. Sometimes I'll open a window in the winter, when it's below 50-deg outside, and I may flip the heat on to warm the place a bit after closing the window.