I am a little concerned that, if her CogAT profile is legit (and it seems that it may be, since it lines up with classroom experience), she may be presenting with a second exceptionality. The transition that happens mathematically at 3rd/4th grade is that they move on from basic arithmetic facts to problem solving and using those facts. You mention that she struggled to acquire automaticity with math facts, and report a significant relative weakness in quantitative and nonverbal reasoning, only slightly above average, which suggests that there may be a true vulnerability with regard to mathematical thinking. The difference between her verbal and nonverbal/quantitative abilities is not insubstantial. In particular, the reports of making careless errors and not paying attention in math (in a child who, I take it, is normally age-appropriate in attention) suggest that she may not be as automatic in math facts as she appears to be when math facts are assessed in isolation. The presentation teachers report is consistent with a child who must expend a significant amount of cognition on basic calculations, which means that sometimes she can't devote enough cognition to problem solving, because she's busy multiplying and dividing, and other times that she loses the basic facts because she is using her thought processes on the new, more sophisticated math skills.
The sense that math is both too hard and too easy at the same time is telling.
I would suggest that, rather than either allowing her to be moved down in math, or fighting the placement per se, you might consider requesting a special education evaluation for a possible 2e.
