At my DS's school at the end of K, they did their reading program's assessment and it has many categories like work decoding, comprehension, vocabulary, etc. and the lowest score he got on that was his reading level. So, for my DS it was 3.9 so they said 3rd grade. His MAP for the end of K was 200. His school ability grouped for reading and he was in the highest group of second graders when he started 1st.
Yes, the summer growth is not typical on the MAP but similar to my DS's math MAP growth for the same time. I would look at the Fall K also to get an idea if your DD is actually growing much in school. I think the typical growth (as NWEA reports it) for a year on the MAP is around 6-7 points.
Finally, I don't really think the teachers understand above average MAP scores as much as we think they should. I think schools mainly use them to develop a cut score for passing the state test and kids who are above the cut score they really don't have to worry about. We tried to have a conversation with my Ds's teacher last year using his MAP to encourage some acceleration and her eyes really just seemed to glaze over. We took the printout that showed where he was for each grade level and and even after explaining it to her, it did not seem to register exactly how high that was.
But based on those MAPs, I think your DD definitely needs some acceleration in both reading and math.
