Mike, Spraying water into the air definitely does work. I did that several years ago in the minnow greenhouse. In a sealed area the humidity quickly goes to 100 percent and evaporation is not a problem. I don't want any spray on the waterlilies ,so that isn't an option in this case. I've also used a circular shower curtain with water spray inside of it with some success. We'll probably never know exactly how well any of them work without a side by side test. It will just be a judgement call.
Waterbug, Solar water panels with underground storage would heat the ground inside the greenhouse and maintain a more stable temp. You also need to be able to vent excess heat when it's sunny.