Platypus got to this first.
For achievement, I prefer tests that have WISC-V-linked norms, such as the WIAT-III and KTEA-3, for LD evals. In general, I find the KTEA-3 to be better both for younger children, and for children at the upper extremes, as the floor means both that some younger children (below age six) have no opportunity to demonstrate certain areas of strength, and that some younger children's weaknesses are obscured by the limited expectations, and because the item set design of the WIAT can create artificial ceilings for very high-functioning children (notably in reading comprehension and oral reading fluency). In the case of your DD, these may or may not be issues. She is above age six, so she would have nearly every subtest. Reading is not her strength, so she is unlikely to have her reading peaks flattened. The concern in her case would be that raised by platypus, which is that the expectations are low enough that some weaknesses might not be picked up. I'm not as concerned about this as I might be with another child, though, since you mention that she is still struggling with kindergarten-level phonics. That is likely to show on WIAT testing.
The KTEA-3 has a larger pool of phonological processing assessments, if the examiner chooses to use them. The WISC-V actually has a few phonological processing tests, as well, among its supplemental tasks. I would agree that the CTOPP is among the better instruments for this, and that the evaluation needs to probe for higher-level phonological processing skills. I also like the PAL-II, for assessing dyslexia/dysgraphia.
Both the WIAT and the KTEA have measures of reading and calculating fluency, though the KTEA has more finely-graded reading fluency tasks for word recognition, decoding, and silent passage reading. The WIAT has gross measures of single word reading fluency for word recognition and decoding (results in quartiles), and an oral reading fluency measure that includes speed, accuracy, and their combination.
For a mathy child, the WISC-V is significantly better than the -IV, in my opinion, especially if a few additional subtests are given (especially Arithmetic, which allows for the ancillary quantitative reasoning QRI to be calculated). If some other phonological or auditory working memory measure is not administered (such as in the CTOPP or WRAML-2), I would also want an additional working memory subtest (Letter-Number Sequencing) to be administered, in order to obtain the auditory working memory index (another ancillary composite AWMI).
Alternatively, you could pursue an evaluation that is based on the WJ system, with co-normed cognitive, oral language, and achievement measures. You would still need supplementary phonological processing, as the WJIV PP tasks are as limited as the WISC/WIAT/KTEA measures. (I.e., sensitive enough to pick up substantial deficits, but not necessarily subtle ones.) The WJ can include the skills, application, and fluency measures that would likely be important for your situation.
For any of these assessment instruments, providing your evaluator with a thorough history and description of your concerns will be essential, as that is the primary determinant of the components of the assessment that they will select. I am not offended by parents naming specific instruments (though I can't speak for other professionals); you should feel free to bring up any suggestions or rumors you've heard from random posters on the internet.
