I'll second the suggestion above to pursue private neurospych testing or at least some type of private, comprehensive educational eval. Your dd has an ADHD diagnosis, and you also suspect some type of 2e issue may be impacting her ability to complete her work as quickly as her peers. A neuropsych eval will not only give you test scores, but will also give you important feedback that will help you to understand what the test scores mean related to the behaviors you're seeing (slow to complete school work). It might be a working memory issue, it might be a focus issue, it might be a fine motor issue... really, it could be any of 1000 things, and having an unbiased and comprehensive look from a professional will help answer so many questions. You will also get a report outlining the accommodations (as well as remediation if necessary etc) that your dd needs, and that's where you begin with advocating - with a professional report in writing, as well as the knowledge you'll gain through the eval.
I also have found it helpful to look forward past the immediate school situation when thinking about what to do in situations like this. Right now you're focused on how to get your dd into the GATE program in 4th grade, but the CogAT testing for that program isn't the only place in her life where the challenges she has (ADHD, possible something else impacting processing speed etc) are going to impact her ability to show her full knowledge. At some point in time she'll most likely have to take timed standardized tests, eventually she'll be taking College Board etc tests, chances are that in middle school and then later on in high school her homework load will increase... things like that. The earlier you start implementing accommodations and the more you understand and have proof of why they are needed, the easier it's going to be to have them in place and not have to fight for them when they are going to count. You're seeing a bit of that "deadline" looming with the gifted program admissions testing - it *is* possible to get accommodations for the CogAT such as extended time or oral response etc. It's *not* an IQ test and it's not a test designed to tease out learning differences, so your school should be able to give your dd accommodations when taking it - provided you've gone through the process of requesting accommodations for *all* testing (classroom and state testing etc). It sounds like your dd needs extended time (and she might need other accommodations you're not aware of). All of this, from my perspective, is reason to pursue an outside eval, and to pursue it now, not later.
Best wishes,
polarbear
