Hmm, the problem with these is that nice, awesome, wonderful and beautiful all refer to traits that are too small in scope or too vague to make good identity claims.

I would argue that 1) "too vague" is just a subclass of "claims to be more objective than is warranted" and 2) "gifted" is in fact as vague as the other examples.

I think what you're telling me in the last paragraph is "Making claims about your IQ makes you sound dodgy because people feel really skeptical about IQ scores."

Yes, but that's not all of it. The point is that because people are skeptical about IQ, making a claim about your IQ says (to such people) "I think I am objectively better, but I'm basing that claim on something which cannot support it".

I want to try a different angle. Two questions:

Three, sir.

If you do not see any way to make such a claim without a high risk, then why do you think that is?

Because you can't disentangle such a claim from a claim of being objectively superior (and specifically, an unjustified claim of being objectively superior). Being nice or beautiful can certainly influence your personality, views, or lifestyle and you can't go around claiming those either. It's not a problem unique to giftedness.