In general there is no problem at all using Open tickets on valid carriers other than the one specified on the ticket. The ticket is clearly endorsed "Valid on BA/AA/CX/QF/IB/LA/etc only" and 9 times out of ten you can just present the ticket at check-in to the airline that has your reservation.

The only time I had to get a sticker endorsement (from AY to BA) was at HEL where AY were doing a pretty poor job in general of demonstrating that they were part of OneWorld (clueless on lounge access with a CX Diamond card, etc.)