I picked the brain of one of the best permit guides in Belize over a week and his feeling was that Permit would usually take the crab on the drop. He wanted us to strip the fly at mid-depth until the permit saw it and then stop/slow down, try to keep the line tight, and watch for a pickup.
I noticed the Permit generally lost interest in the fly once it hit the bottom and the few takes we did have were on the drop.
He actually had us using those "arrow" shape EP crabs but only on the deeper flats. They definitely sink a lot faster and have a more vertical profile on the drop. Maybe this is why the more streamlined patterns are coming from the Keys where they generally fish deeper flats?
Incidentally the bonefish had no interest in the crabs on the drop but would get all over them on the bottom. Go figure