I don't mind replacing food and water for them but sometimes i wish i didn't have to lift up the screen and let the humidity out, knock stuff around and what not. This idea, i think, would only work for custom tanks, like the ones made from old cabinets and would be super easy to manage. This one is the dry food one, the wet food dish is much simpler.
Basically a floating dish that is fed similar to a cat feeder.
The food storage bottle is on the outside of the tank with a tab that lifts or drops the angle of the dispenser.
Push the tab down...
...and the gate closes
But with crabs they never eat the whole dish and since its so humid, the food gets moldy, even if it is dry food, sooo the bottom of the dish can get pulled aside to drop the food down a tube.
The tube leads out of the tank and drops down into a wastebasket that you can throw out or dump into your compost.
On outside of the tank on the next wall you have your pulley that connects to the floor of the dish.
Everything would of course have to be made from crabby safe materials, i figure at the very least, wood with a silicone layering. it would also have to be sturdy enough to hold their weight and prevent them from wriggling out of the tank in any way. It would essentially be a part of the wall so cleaning could be an issue. The dish floor would also need a track to slide on to make sure it doesn't pop out. I could get creative with the outside latches and pulleys, but the hinge on the inside of the feeder where the dispensing slide is that would be tricky. Emptying and dispensing would have to happen when the crabs are not on top of it but I think the basic idea is sound, has anyone tried this yet? Is this totally outlandish?
The things we do for our crabs!!!!! 
Neat idea!