Never have been downgraded from P (which is business class fare, just discounted) on LH/LX/OS. Just check-in early and get your seat confirmed.

Wouldn't worry about that. And I guess the J cabin experience with LX and OS will be much better if you are used to BA

Btw. Avoiding connecting in LHR already makes the flight more comfortable in my opinion. Both ZRH and VIE are quite good airports for connections.