It is more a question of the value proposition ($10 lunches?) and considering the consumption of parental vacation time. Last summer DS7 enjoyed a hands on equations camp setup for grades 1-6 for a week at $200 and the top group matched his level even if not his passion.
Regarding qualifying, he also has a similar scatter issue. One of the instructors started the local kid's math club, I might see if I can catch a minute with him about how big the applicant pool is as that might imply how flexible they are on whether a maxed math achievement with a near IQ might work.
You might be surprised at the quality of the middle schools math clubs/camps you are talking about. My ds school has math camps all summer. They have 2 different classes and they are packed. They go over a ton of discrete math topics at a very quick pace. They have several Math counts test and several team competitions during each week. Even the best kids are challenged. On Friday they set up the gym and have a mock team competition... they call it the guts round competition, kind of based of the MIT type competition. It's worth it just for the kids to hang out with other mathy kids. I am sure it is not up to par with the camps you guys have been looking at but it is very good exposure. Just a thought.
It sounds like you are in far more "intellectual" areas than we are. The gifted middle school (within a regular school) may be a bit of an oasis here, especially since it is, quite anomalously for around here, the only gifted school that has not been placed in a dangerous part of town, so it has a much higher participation rate of qualifying students. So their math club would be pretty good. But apart from the odd bright spot around where we live, just as some people live in "food deserts", we are living in an "intellectual stimulation desert". There's certainly not going to be anything like what you two describe.
So I have definitely not pushed it but it would be nice if she had more interest. On the other hand, I wonder how a camp like Epsilon would handle it if a kid ended up not wanting to be in class all day--probably it doesn't come up much though because given the cost I bet people are good at self-selecting.