No luck at all. Only can book what shows on BA. AS search is easier, so I cross check with that before bothering to go through the process.How did you go with this? The Alaska site often shows phantom availability, drawn from QF's inventory which is only available to QF members (a good example if the recent 'wide open' SYD-DFW which is available to QFFF members, but was not available to partners).
For accurate availability of what Alaska might be able to book, cross reference with the JAL booking tool. That only shows what's available to partners.