First, I'd say that trusting your own judgement on your DS is probably the best way to go. You know your child better than anyone could, and you're coming at it from a very solid background yourself. I myself forecast my DD's RIAS score, and missed by just a few points.
If anyone has a better solution to the anxiety/negative self-talk sitution I'd love to hear it, as this has been a battle with my DD12 her entire life, and it's not getting any easier. However, these are the things that seem to help, at least temporarily:
1) Ensure you're building a growth mindset, because perfectionism can be at the root of the negative self-talk. Accept and encourage failure. Model that by taking on challenges yourself and struggling with it, and let him see you do it. Put him in some kind of activity where failure is expected and is a necessary part of the learning process - music, sports, etc. Laugh along with the failures while celebrating the successes, and remind him of the many failures that were necessary to achieve those successes.
2) When he makes an outrageous negative claim, help him build a more accurate process for self-assessment, by asking him, "What's your external evidence for that?" And when he struggles with that, begin offering evidence that is contrary to his hypothesis.
3) Recognize that sometimes it's not about the statement at all, it's just him expressing of a strong negative emotion, and help him cope with that as appropriate.
