Make one of these. Duct into tent. Problem solved. Just drop frozen gallons of water in and flip the switch.
Swamp coolers with cool water don't work well in high humidity as they add a ton of humidity. Ice would simply be a pain in the ass and add humidity.
I beat the heat in what was once my grandfather's office with a trip to Lowe's. I don't have a humidity problem here, especially in summer when it is an average 70%-95%. The a/c has a built in dehumidifier if I need it.