Honestly, I've asked the first question myself to alot of people, I get the same reply of "Hit max level as fast as you can and do DC/DF." (Which are the last two dungeons. In the mean time, just do the dungeon according to your level. Faster you level, the better dungeon you can get in to. You could sell your boxes or open them up. I usually just open them up. Remember, you get 5 coins a day and they don't stack up.
I read on the forums that some Titans did that but I'm not sure why you would want to other than for funsies.
Chiharu is my best friend.
Didn't know this place still existed.