Things I did yesterday while waiting on a single queue:

- Sent my retainers on ventures and managed my MB stuff
- Killed an S rank
- Did a FATE
- Did three levequests

And, amazingly enough, I managed to hit 'Commence' when it popped. The idea that you have to sit around in a sanctuary and not do anything while you're waiting on a queue is patently false. You just have to be intelligent about what you choose to do and not start something that you can't extricate yourself from in 45 seconds.