Chilling a cake in Texas only causes it to sweat, pools of sweat. The humidity and variations in temperature throughout the day make for a disaster of a cake. The only recovery from chilling the cake is to start over with fresh frosting. Otherwise the cake will slide apart.
You may wanna try spritzing the cake with a touch of cornstarch use a pump spray sorts to coat very lightly before refrigerating and dab the condensation off with a kitchen towel and avoid drastic temp changes hope this helps. 😊 and always store in air tight containers to combat condensation and bacterial changes too.
I am in Iowa, and I know we are hot as hot as you get, but the humidity on top of heat here can make it next to impossible for a few weeks in the summer:(