The hat indeed belonged to GG, but THEY (all the founders, including SS) put the brains in the hat so it could sort a student properly.

If a "true Ravenclaw" had been in Harry's situation, no doubt the hat would have supplied a solution befitting RR, a witty, thinking solution.

The sword kind of makes me think GG favored the physical tactic of killing the monster rather than out-thinking it.

Very effective against a Basilisk, don't you think?

Harry may be a "true Gryffindor", but he represents the best of the other houses too: out-thinking the dragon, etc.