M&TSI vs. Boys Nation

This spring, I was accepted to M&TSI and decided to attend. A few days ago, I was elected governor of CT Boys State and invited to attend Boys Nation. M&TSI runs from July 7-27, while Boys Nation runs from the 19th-27th. Which should I do?

Here's some other relevant information:
- M&T is my dream college program (the actual one, not the summer one)
- I have already paid for M&TSI, although my family is quite stable financially
- I was really good at Boys State; I won by a very large margin for governor, so I think I would have a shot at winning a big position at Boys Nation.

The way I see it, I have three options:
1. Attend M&TSI and decline Boys Nation (safest, I'm leaning towards this at the moment)
2. Attend Boys Nation and withdraw from M&TSI
3. Try to attend the first 11-12 days of M&TSI and then leave for Boys Nation.

I assume that nobody who will see this has attended both M&TSI and Boys Nation, but if anyone has insight on any of the following questions, I would love to hear it:
- How valuable is Boys Nation on a college application for someone who is interested in studying business and computer science (not politics)?
- Will turning down/leaving early from M&TSI significantly hurt my chances of admission to M&T?
- For anyone who has attended M&TSI, would it be reasonable to leave the last week of M&TSI, or would this defeat the purpose of the program?