If the sand would stay mainly dry in the summer, then that would work, and stays cool.I'm in a predicament with my run. It is a 9x12 covered run. Up until now it has been dirt except over winter I did DL. It is way too hot here in the summer for DL as it produces too much extra heat. I've lost several chickens lately and my vet thinks it might be due to pathogens they are picking up in the soil. Thinking about sand but I've heard mixed reviews about that too.
Come fall, you could pile leaves, wood chips, etc., up and use the DL method. You shouldn't have to remove the sand.
Then rake this out in the late Spring, mulch your garden, and replenish the sand.
It does seem like a good idea if you had a necropsy done on at least one chicken that dies to verify what the cause of death is?