You don't seem to realize that you don't need to pay for lhr-zrh and ist-lhr.

You can add those on to your award for a small fuel surcharge on BA.

So book lax-lhr-zrh and ist-lhr-lax on aa.com and then pay cash for any flights inside of europe you want.

It's a shame you don't have *A miles you could fly on TK or LX although the new AA product might be slightly better.