Glad you added a new post to this thread...I remembered that someone had asked me a question a while back, but didn't get a chance to answer it at the time, and then couldn't find the question!
Taking into consideration a number of things you've shared, it sounds like the critical executive function that impacts your daily life may be the one we call shift or cognitive flexibility (switching, on the assessment you completed). This can result in or combine with low processing speed to generate the "slow but accurate" presentation you describe, as well as the single-minded focus that sometimes causes you to respond to the unexpected poorly, late, or not at all. I find that it can be helpful
1. to be patient with yourself. Extend some grace to yourself when you realize after the fact that you've arrowed past something that you wish you had responded to. And then try to think if there's a more planful avenue still open to you to go back and offer an appropriate response. Sometimes there will be, and other times there won't. That's okay. In the second case, look for any small skill that you might be able to learn from it for a future similar situation, such as a short, civil comment you might be able to make, either internally to yourself, or aloud to the other person, to communicate that you would love to respond further, but after you finish this task. To do this, it helps to
2. prepare a menu of standard, pleasant responses to situations that arise repeatedly. You note that you don't have difficulty with things you already know; it's novelty that throws off your cognitive flexibility. So, when you encouter a new situation, learn what you can about appropriate responses for it, and practice them (preferably with a friend or therapist) until they don't feel new anymore. Quite a number of mental health professionals can help you generally with what they'll recognize as social skills training/coaching, but for more tailored practice, you'll want to detail the kinds of situations that affect you the most, so your practice partner can work with you on those.
3. Managing your environment also helps, such as by learning some verbal stalling tactics, to give yourself more time to process incoming information and shift your thinking. Some people use phrases such as, "give me a moment," "explain that again," "so you're saying...[and repeat or restate what they just said], or even take the direct approach with, "let's slow this down."
Both cognition and executive function are important to daily life needs. One way to think about it is that EF is the collection of skills that allow efficient, on-demand access to your other skills (including cognition). And yes, just as most have patterns of strengths and weaknesses among cognitive skills, one can have strengths and weaknesses among the EFs, such as good planning but weak flexibility. It's also important to note that we've made some artificial and arbitrary distinctions between executive and cognitive skills. The reality is almost certainly that they are intertwined (and, well, they're all in your brain!).
All formal measures are attempts to access incompletely understood and interconnected skills in a complex system. IOW, none of them are ultimate descriptors of you or your abilities. That being said, the FSIQ does appear to be the most robust predictor of academic function for most people--but you are not most people. EF is probably a better predictor of general life function, since it affects all dimensions, but it's also a set of skills that can be learned and accommodated. Which is to say, it's all of the above. The GAI is a purer measure of reasoning, but the FSIQ includes estimates of the impact of some EF skills (in the form of the CPI). One might say that, when your EF vulnerabilities are well-accommodated or remediated, you are capable of functioning at the level of your GAI, but when they are not, your performance is likely to fall somewhere between your CPI and your GAI.
This should not be discouraging, btw, since it simply describes one variation of the state of every finite, imperfect human, and underlines our need for each other, and to seek completion in community.
