Simulated Government - Ceasing Power?

Hello everyone! This doesn't really fit in any other category but I'm looking for some advice and political knowledge so I figured I'd stick it here!

From June 8th to the 14th I'll be participating in Texas Boys State. In short, it's a prestigious leadership camp(only about 800 are selected in the state) in which the delegates learn about the democratic process and other things.

Everyone at Boys State will take on an assigned or elected position just like in real life. The highest elected position is Governor, and whoever receives that title goes along with another individual to Boys Nation to represent the state in Washington D.C. and it looks EXTREMELY impressive on college applications, which brings me to my order of business.

In order to take the position of Governor I'll first have to receive 30 signatures from people in my party(students are assigned to one of two political parties). Somewhere along the line I'll have to 'campaign' in one way or another and gather votes, and sometime during the program I'll have to give a 10 minute speech. I've been trying to develop a strategy to essentially take power in the democratic system, and I have a loose idea but I'm clearly no expert.

My current plan is to create a system of political favors. "Hey, I've got 30 supporters. You vote for me for Governor and my supporters will vote for you for _______." I know the logistics of making a WORKING system like this would be difficult, and I'd have to promise a position to more than one individual, which is why I currently plan on manipulating the system. I believe playing off of people's selfishness is my best chance at being elected.

What kind of a strategy would be successful and how could I plan it out and orchestrate it? I only need a system to keep my supporters happy up until the vote because after that it doesn't matter. Any ideas are welcome, I'll surely need them.