JHU CTY summer camps may be good for middle schooler. She may feel too restricted by the rules when she is a HS sophomore or junior. In opinion, she should try something more substantial and "intense", as you said.
If she is into math (even just a bit), she should try a math camp. There are plenty of to choose from. Find one that need a entrance exam which weeds out most kids who just want to have fun.
There are certain stereotype for girls who go to a math camp. Some girls don't care. My younger daughter went to a math camp in Boston area for two years. She wears it like a badge of honor. Like everywhere else, the girls can be cliquey. It requires some effects in order to have a good time. But the bonding is very strong even after 3 years. Most of them ended up in fabulous colleges on the east coast.
