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No wonder your basement humidity is so high, you have the window and doors open. You mention your concerned about keeping the house around the 70 F, does this home have a HVAC unit ? With the AC on you will reduce your room humidity by the simple process that the AC uses to cool the air, it pulls moisture out of the air that's why you see the little drip line near your cooling unit.
A simple and cheap dehumidifier available at all big box stores will also help reduce your humidity levels. Most have sensors that you can preset the desired humidity levels, they collect the moisture from the air and collect it in either a tank for your disposal or they can be plumbed very easily directly into a floor drain etc...
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