It really may hit none of your criteria except for the 2 week time frame, but I thought I'd throw it out there. It's called Summer's Best 2 Weeks, and is outside Pittsburgh
My nephew is 9 and loved it, and it came highly recommended from family friends.
It's focused on having a variety of sports and allowing the kids to compete individually, in groups, and among the whole camp across all its age groups for the overall trophy.
It's also co-ed but has a heavy overarching Christian mission (founded by Presbyterians, but the counselors aren't required to be any denomination).
My nephew is a sports prodigy but is addicted to winning ruthlessly. It seems like he had a blast, but also maybe they started to get through to him to be a good sport and kind neighbor regardless of what happens... Which is impressive if it sticks.