Yup. It's the best solution as far as I can tell.
As I said in OP (but may edit out later, so I'll post it here for posterity or something):
Includes sideways-standing mount point because you can't lay down when sitting up in a vehicle, unless everyone is able to do that and stick their heads through the walls. An alternative was to use the death animation but that would mean that turning around puts your head through the wall. I also didn't like the idea of having the patient sitting bolt upright on the bed. So, you're standing sideways, meaning you can spin like a turbine on your way to the hospital. I was almost upset about this but it's not much weirder than anything else in Blockland.