While it depends on your goals and what you want to get out of this game, I think it's really difficult to get things done in such a small window unless you could coordinate with others to be online at the same time.
XP is probably your best bet because there's always something going on in Abyssea and even if there wasn't you could solo your XP.
But if your goal was to improve your gear, I think it would be troublesome. As an example, if you wanted to do seal farming, you'd probably want at least one other person. And the entire process from shouting to fighting would very likely take longer than your window of time. Something like Dynamis would be tough too because it takes 2 hours, although it does have the advantage of being a solo or very low-man event.
If you have the flexibility it may be preferable to play less frequently but for larger chunks of time. Whatever you decide to do, best of luck.