I'm quite certain BA doesn't have 24 hour service in the UK and in Europe, and probably in the US as well!

I suspect this is part of the reason that the OP's requests were met with bewilderment by BA, although in mitigation, BA should be forthcoming if a flight to an originally ticketed destination (whether for cash or redemption) is cancelled.

I suspect also that Alaska, as a codeshare partner outside of oneworld, adds to additional 'issues'. Nice airline though.