I'm responding to this to bump it back up. There are lots of folks on here who know way more about testing than I, but I'll throw in what tiny bit I know from our own WPPSI testing and recent dyslexia testing, which included the CTOPP.

To help the group in answering your question - what tests did she have done in K, and what tests has she had done as part of this reading study? Are you looking for additional testing, or just interpretation of testing you've already had done? (Or maybe you're not sure which you need, in which case, this group should be able to help you.)

Since I don't know much about testing, I'll tell you what we've had done and the results we've gotten out of those tests that may be somewhat pertinent to your DD. If you've had similar tests done, but no helpful information out of them, finding someone to interpret them may be more cost effective than more tests.

Based on your original post, and on our own results from our WPPSI and dyslexia testing, I'd say you've likely identified the culprit - her short term memory is not at the same level as the rest of her abilities - and now you need to know what to do about it. The tester who did DS's dyslexia testing a month ago gave us a 14 page report with conclusions and recommendations. It sounds like you need those types of recommendations on how your daughter can get help with her short term memory so school is not so exhausting.

So here's what we got out of the testing we've had done:
- Our DS7 had WPPSI-III testing done at age 5.5. Testing revealed a gap between processing speed (50-somethingth percentile) and other subtests (98th/99th percentile). The tester told us how this would likely play out as he gets older and gave us strategies to address it. Working memory (which I think equates to short term memory) is on the WISC, but not on the WPPSI. Others on this forum can hopefully tell you whether you get enough additional info from the WISC to do IQ testing again, if your DD took the WPPSI the first time around.

- We started to see the processing speed problems play out over the first two months of 1st grade this year. We had a dyslexia evaluation done, where they were able to use the previous WPPSI-III testing. That tester administered the following: CTOPP, GORT-4, TOWRE, TWS, and WJIII. We received a 14 page report from her with her conclusions and recommendations at the end. The results were that he's not dyslexic, but that his processing speed is playing out in his reading and that he probably also has lower working memory. His scores on most tests were quite high, but it took him an inordinate amount of time and concentration to get those scores. He scored 37th percentile in the Memory for Digits subtest like your DD (but scored high on the nonword repetition subtest).

- We got a set of recommendations primarily focused around building his fluency through tutoring and an online program, but also recommendations for his teachers to implement, including removal of time limits on tests and not grading on spelling unless it's a spelling test. School cannot provide any kind of tutoring because he's performing above grade level, so we're doing that privately, but they can implement the other recommendations. It will be helpful for you to get similar types of recommendations for your DD, based on whatever her specific needs are determined to be.

Regarding your last paragraph of your post, it sounds that you suspect there's a gap between her short term memory and other abilities and that the CTOPP is accurately revealing this. That sounds reasonable based on the rest of your post, and I'm not sure I agree with your DH. If you find a good educational specialist in your area, they can also help you decide if the current testing you have is adequate, and you just need them to interpret them for you and provide some recommendations, or whether more testing would be helpful.