What's your relationship with the principal like? If it is really good, it might be worth requesting another meeting and talking through the presented options. (I'm basing this on your comment that he's read the research and acted accordingly.)
We found that having outside data helped us. YMMV. In your case, it sounds as though it might be really helpful to have test results showing where your daughter is at in math. (Objective tests, not the one that she might be given again at the school.) Also, be aware that some educators think a passing score to move on needs to be 100% in these circumstances. We were fortunate that the educator who gave end-of-year tests to our DS thought that 80% was the bar. (DS scored higher than that, but the tester said if it was in the 80s, we would discuss a plan to accelerate while we would fill in "gaps" at home.)
You may also find that test results could qualify your child for gifted programs (weekend camps, etc.) outside the school district.
The principal is pretty awesome. He's all about accelerating kids who need it.
The problem is that our district offers honors math in 5th grade. It's a compacted math curriculum including all of 5th and roughly 2/3rds of 6th grade. The program is great (DD11 did it this year in 5th grade and qualified for a math skip next year), but the principal was concerned DD8 would not qualify on the honors test given at the end of 4th grade. He wants her to be at the top of her class still and be doing the honors math. I agree. I think she can handle the honors curriculum.
The math curric. leader already gave DD8 the honors test back in Dec. when we were deciding whether or not to skip to 4th grade for the last half of the year. She didn't score as well as they liked to see, but passed all the 3rd grade material. The math curric. leader said he can't keep giving DD the test over and over, so when she takes it again, that's it. And it will solidify her placement next year.
I think she would pass it if we gave it to her right now. But I want to be certain, so I opted to test this summer after we review the math. I didn't want to jeopardize her placement or create a stinky situation where I had to fight to get her re-evaluated in the case she didn't pass. It's been a sticky situation.
If we had followed the IAS, I believe she would have qualified for a skip. It was just the honors math test that held her back. Hindsight is always 20/20, you know, so looking back I wish we had subject-accel her for the last half of the year, then re-tested for honors placement by May. I think she would have done fine. Instead, she had wishy-washy "enrichment" in class plus some teaching we did at home here and there, and I think she STILL would pass it.