... I know she needs this program and I don't want her to test out of it and be left out forever more.
Is there pretty much a HG program or the regular classroom and nothing in between? We have the opposite problem where I live where there is a GT program that admits nearly 20% of the students (top 5% achievement in any area or good leadership skills, or nominated by a teacher, or...). It doesn't meet the needs of the more HG like the kids served by your program, but it probably is a reasonable fit for those more in between kids.
It is a bummer when all that is available isn't good enough for your kid and I suspect that those kids who just miss the cut for whatever the program is are the ones whose needs really don't get met.
As far as telling if she has high conceptual knowledge of math, do you know what IQ test they are using? My oldest, who is more verbal like you describe your dd, took the WISC-IV when she was 7. She doesn't have the kind of math conceptual understanding that her younger sister does, but she's been a pretty high achiever in math since she started getting taught a more reasonable amount (mostly post-skipping a grade). She also would have done well enough on the PRI (the non-verbal part) to make the cut your program has had she not totally bombed the block design piece. That was due to two things for her, though, that may not apply for your dd: she's slower in processing speed and it is timed, and she froze and refused to complete the test handing the blocks back and saying that she couldn't do it and was done. I'm not a scoring expert on the WISC, but her three sub-tests were at 19+ (99.9th+), 17 (99th), and 8 (25th -- this was block design). I suspect that if the 8 had been even much above 10, she'd have hit the 140 point you'd need.
Point being, kids who are not necessarily mathy can do very well on non-verbal tests, so I wouldn't rule out that she has significant abilities in that area even if arithmetic isn't super high right now.
