As a nice data point of two cards in under 30 minutes:
Applied for #1 - Pending
Called in, was transferred a total of three times eventually to Fraud. Approved
Applied for #2 - Pending
Called in, approved for 5k. I didn't want additional credit, so just asked to move from my first card.
This was all in under 30 minutes. No need for two browser or fast finger tricks...etc.
How soon can I rinse and repeat? I need an emergency stock pile of Alaska points in case AA screws us all over.