If I understand the OP correctly, your DS has been diagnosed with 1e, apraxia, and you're wondering, based on certain behaviors, if he might have a 2nd e of giftedness, though the testing so far does not bear that out. Is that correct?
If so, based on what I've seen here, it sounds like you may be on to something. The positive traits you've observed indicating giftedness (thinking about big issues, existential angst, mental growth leaps, emotional sensitivity, empathy etc.) are good reason to believe he may be, and the traits negating that hypothesis (forgetting names, routines, or what he's supposed to be doing, extreme scatter on evaluation scores) would seem to me that they can be explained by a single factor: lack of sleep.
I have endured sleep deprivation over a period measured in months, and seen how it affects cognitive function. People thought I was an idiot, and based on my performance during that period, they had good reason to think so. I met my future DW when she was going through a similar episode, and I liked her well enough at the time, but seemed rather reserved and didn't joke much. Then she started sleeping, and holy {bleep}, she's hilarious!
So, if I were in your place, I'd focus primarily on the sleep issue, and then see what sort of child you have once he's sleeping regularly. It could be that these episodic leaps are linked to times when he's sleeping better.
