Well there's the cause of the engine shaking like dickens:
Fuel pressure is provided by a primary fuel pump with a backup fuel pump in parallel that kicks in if the power to the primary fails or if the fuel pressure drops below 20 psi. It doesn't matter what the fuel pressure is though, the injectors will only deliver fuel on the intake stroke.
During an ignition only shutdown the fuel system is still working at 100% all the way through the shutdown.
It actually does matter what the fuel pressure is. There's a reason it's called "idle" cut off. If one of your pumps is pushing fuel at 'high' pressure into that standard TCM FCU at idle, some of it will be getting through the FCU into the manifold and the valve in it will never close to provide that 'clean' shutdown. That, presumably, is why you have to switch the 'whole' FlyEFII system to get a 'clean' shut down.