I would maybe just eat the Potatoes and try something else for long term storage. Sweet potato, Taro, Cassava, or a type of Dioscorea Yam may all be better for storing at warm temperatures than the potatoes.. Those all come from tropical areas and when cured they can store for a while. Maybe even just leave them in the soil if you don't have pests or hard frosts...
The True-Yams store without refrigeration in Florida, according to this person here :
I've heard of someone growing Taro in Texas as well :
http://taroandti.com/2008/09/21/taro-survivors/
Cassava might be worth a try :
http://www.floridasurvivalgardening.com/2012/09/survival-plant-profile-cassava-king-of.html
Not sure about any of this since I've never farmed in Texas, just some ideas =)