Will they really provide the car service from A to E if you're actually arriving into ZRH, without a connection out..? I guess if you insist they might do, but it's definitely not meant to be used this way..

I'd probably head directly for the train to the E Gates by following the "transfer E" signs (Assuming your passport allows unlimited entry/exit into Schengen, that is..) and visit the FCL E there, then head back by train again..