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.