I don't see what isn't Fi-seeking about being a 6.

Type 6

That's probably the best, most detailed and thorough Enneagram site I've ever seen, and what they describe sounds precisely like Fi-Dual Seeking behavior. Gamma NTs could easily be 6w5s (despite the fact that I think of ILIs as mostly 5w6s), and Delta STs 6w7s (although many LSEs are classic 8s; maybe these would be more of the Te subs).

Joy, I could see you as a 7w6, but it's only even remotely possible if you're sx/sp; that decription does seem to fit you, and the 7w6 sx/sp I know (an ILE) has a lifestyle and general social outlook that is not much unlike what I perceive yours as being.