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Please take a trip to the Martinique island and see for yourself how humid it is and how often does rain.
The SAD syndrome can be attributed to small containers with poor air circulation and organic substrate which decomposes if wet. Small spiderlings are fragile and can desiccate easily, also...
I know I'm late, but I think your sling died of dehydration, that enclosure looks bone dry, a water dish on the ground on the opposite side of the enclosure for an arboreal sling :(
I recommend a taller enclosure, ceramic media for substrate, a gazilion holes all over the place and spaing a...