IIRC, the 15 seconds delay is only offline. Even if you are alone in the Age, you have the same time speed as in MOULa online (1 minute for the door and the cloth number is displayed as soon as you click on the cloth), and you need other people.
So, apart if you like cheating and use /jump, you can't do it alone.
Offline, you have about 4'30 min to press all the cloths and 15 sec before the cloth number is displayed. This way it is nearly impossible to run out of time
Actually you can do both ages offline in less than 1'30 min and can see (or guess) almost every cloth numbers in 3 seconds...