I fully support your adventure, a very dear friend of mine and amazing rider down here just won Miss Rodeo a month ago, she's 16, and this was her second year of trying. She is a very decorated rider and consistent high pointer. She rides both English and Western and places very well in both.
However, having said I support you, I honestly don't think you'd win and I'm not sure you can even qualify as an English rider. What did the rodeo say about riding English when you asked them? EVERYTHING about rodeo is Western. They are looking for someone to represent the spirit of the rodeo, not just someone who can do the things required to win the competition.
To encourage you to "go Western" and help you prepare, here are some things they may ask you to do based on my experience with my friend:
-Do a flag run. You'll need a flag boot.
-Level 1 Reining pattern.
-Queen's run-- flat out gallop around the arena a couple times with a horse that's comfortable with applause; and carrying a flag.
-Mounting and dismounting your horse from the ground without assistance; no offense as I know diddly squat about actual English style, but I'm under the impression English riders typically need help up due to the design of the saddle?
-Quiz about rodeo history and facts
-Give a speech about rodeo
-Beauty pageant, during which certain attire is required, ALL of which is Western-- Western dresses, jackets, hats, pants, belts, etc.
-I think there was also a horsemanship section but I wasn't there for that so I'm not sure.
-Another point in fact: when you win you'll be required to wear big flashy Western chaps to every event you go to as the Queen, and that would look a little silly with the English getup.
My point is, while I totally support you going for it, I don't think it's a good idea to try to subvert a system that is wholly there for the very purpose you're trying to subvert. It's like me showing up at a hunter or dressage show in a western saddle and chaps. Something tells me I wouldn't win.
Go Western! It's not hard to learn; if you can do English, you can do Western.