One tip I was shown from my guild is to get through floor 11 every day. Then next day you kill the boss and get to floor 11 again.
Since the tower carries over day to day your progress will be saved at floor 12. When you win a previous day's tower, you can then re-enter and start a new tower for that current day.
Here are some reasons why this is a good idea:
1) You can near-instantly win any Tower Level 3,7,10 quests the next day. Perfect for if you happen to be busy and would not be able to do your Guild Floor 10 quest. Or have no internet, or travel, whatever. Now you can win floor 12, do floor 1 of the new one so it rolls over and save it for the next day. And catch back up later. This can also help keep you from simply forgetting to do your guild 10 quest...
2) If you cannot always win the tower, this helps you guarantee that you can do your Guild floor 10 quest. Normally if you cannot win one, you are screwed. But by the carryover technique you will have always won first thing, and if you get stuck, you can go ahead and Quit, then catch up the next day. Basically you have 2 shots at winning any guild floor 10 quest this way.
3) If a 2x pwnage points comes along you will get maximum value out of it. Three 2x sessions. Normally if you finished your tower before afternoon rollover and the 2x notification comes along...you are screwed. But if you rollover, you will simply delay tomorrows finish until after the 2x pwnage event starts. Then get a second 2x from the next day, then youd go ahead and complete the 3rd one before the event expires.
The only possible downside is that you are 1 day "behind" in cashing in your gems. But if you ever really need them to hit 2700 gem for a portal event or whatever, you can always go ahead and complete for that day instead of carrying over and cash out.