Yeah, that makes for a tough spot. An example of why people should NEVER buy straight AC.
Unfortunately very few sales people are willing or able to explain why you might want to spend a few bucks more for a heat pump (one valve and an accumulator are the basic difference).
Your house is so small you could go with an "electric furnace", then when the outdoor unit goes your all set for a heat pump. Probably be cheaper than a new low efficiency gas furnace, and the monthly meter fee savings would likely be more than the increased cost of energy source.
Which makes more sense to you? CONSERVATION - turning your thermostat back and being uncomfortable. Maybe saving 5-10% ENERGY EFFICIENCY - leaving your thermostat where everyone is comfortable. Saving 30-70%