I think that you are overthinking this.
There are a lot of very good universities. You might be surprised at the opportunities that are available at “top 200” universities, or even at universities that you have not heard of. You might also be surprised at the high quality of the top students at a “top 200” university. Very smart people go to a very wide range of universities for a very wide range of reasons.
Admissions to top 20 universities in the US is very difficult to predict. They are looking for students who have excelled at whatever high school they are at. They are looking for high grades, high test scores, and great references. However, they do not expect you to fix your high school. They do expect you to have accomplished something. What that something might end up being I do not think that any of us can predict.
Being in the top 5% of your graduating class will not get easier just because you are at a larger school. A larger school will have more students and more students in the top 5%, but it will also have more very strong students.
I think that as long as your parents can afford your current school without debt, you should do the best that you can where you are.
1000 students is not all that small of a school. If there are 250 students in each grade, and if the available ECs are not all that good, then there are going to be students who would be willing to help you start a new club or activity, or probably more likely reinvigorate a club that already exists. Remember that leadership does not mean getting your way. Leadership means making a club better for everyone who participates. If you can take an existing club and encourage people to make it better that is a form of leadership. As one possible example: what could you do to find funding for the robotics club, and can you find people who would help you build a robot that would do something useful or interesting? (This does not have to mean entering a competition and bashing another robot to pieces – but it could).
You should do as well as you can. Keep ahead in your class work. Treat everyone with respect – the people who write your letters of reference will notice. Get good grades. Look for clubs that you are interested in that could be improved and for students who want to help you do this.
Also, keep an open mind regarding universities and colleges. Think about what you want in a university. There are a lot of very good schools to choose from.