AAnytime awards are REALLY expensive. I would investigate all options before buying one... including possibly a business class fare sale.

You will also end up having to pay huge EX-LHR taxes for the return.

If you can book lax-jfk-zrh on 762/763 as sAAver over lax-lhr AAnytime, I would choose the sAAver.

RT sAAver would cost you 100k and rt AAnytime would be 200k.

Also, for BA's inter-europe flights you will almost always find seats. If you found a sAAver award on the dates you wanted, BA's lhr-zrh and ist-lhr will likely be wide open (but they cannot be booked as part of an AAnytime award)

Do you have any other points/miles? Swiss usually opens some business seats a week or so out.