While I cannot comment on the Westermann Door fittings, I can confirm that a tonneau cover and the long nose tower cap are more than adequate protection when parked up. The tonneau effectively seals off the cabin area, and the shower cap adds an extra layer of rain protection - even without the windscreen in place. I just lay it over the Brooklands screens and loop around the mirrors as with the full screen. Yes, you might get a slight puddle in the shower cap if the rain is heavy, but this can be poured away easily before removal and then you have a dry tonneau cover underneath.
If the poppers on the tonneau and doors are not aligned, you can tuck the tonneau inside the door and just rely on the 'top' poppers to hold it in place, but I would not recommend driving with it held so loosely. Or lay it over the outside of the half door, and cover with the showercap as usual.