Hi Jim and Maria, my husband and I have BUPA International insurance. It is not inexpensive but it covers us anywhere in the world we travel. Our agent works out of Panama City, Panama and he is happy to answer questions about it. Contact Gonzalo de la Guardia: gdelaguardia@gmail.com.
You could also, do as you suggest, and have coverage in both places. You will need a resident visa in Ecuador in order to obtain coverage. And yes, this may be more economical for you. If you already have insurance in the States, speak with your company about whether or not it will cover you abroad.
Another option is to check with one of the major local hospitals in Quito or Cuenca and purchase a hospital discount policy through them. I am unsure if you need residency for this — may be a good option for you.