The last time I had to get a "kidnap victim" from car to door, it struck me that I should have put her in a niqab, the extreme Muslim robe with the black net veil over the face. Someone wearing that could be Shibari tied, gagged and blindfolded or isolation hooded, and wearing a couple of big plugs and a six-inch hobble, and nobody would know.
If you don't want them to move under their own power, you're going to need a helper or a heavy sack truck to carry whatever you use. That being so, a custom crate could be made to accomodate any position, from the coffin suggested, to something that requires the sub to be folded up in a tight crouch; the choice depends mostly on how long a journey you plan. Any carpenter can make it, they don't have to know what the box is for: when you get it home you drill the discreet airholes and attach the straps to the walls and floor to hold the occupant in place.