The style contest actually ultimately takes much higher style rating even than that to win the entire thing at the highest ranking. There are several things to know:
Many different equips can be style-upgraded at the fashion forge. This will help. When you go to the forge, you will see as you cycle through the gear in your bag whether they can be forged or not, how much it will improve the style rating, and how much it costs.
You can use any Pretty Betsys you acquire to improve style.
Style improves with levels, so if you level grind some, this will help.
Which vocation you are in makes a huge difference. Luminary and hero class both come with built-in 15% style bonuses to your base stats while in that class, and if you master Luminary that's another 15 extra points again as long as you stay in Luminary.
There are also bonuses for certain combinations of equips. For example, if you equip all four pieces of Platinum gear or all four pieces of Metal King gear those come with style "combination bonuses". There is no list of those combinations in the game anywhere but I'm sure it's covered someplace in one of the FAQs.
So in summary, your best chance to win the style contest is to be in Luminary, mastered if you can, use Pretty Betsys, forge up your gear, and see if you can get any of the bonus combinations.
Sorry it took me a whole day to respond. I've had internet problems today. The fashion forge is actually nowhere near the style contest. There are two; one is underwater in the real world on the south end of the big ocean and the other is in the town of Turnscote. The ocean one actually becomes a zoom destination on the zoom menu once you find it.
Well done. The plush rug with which you get the carpet in Sorceria is the third possible prize out of eight total, so if you want to continue, the rest of the prizes are nice equipment or items, but are not required to beat the game.