Re: which parrot species is best for me ?
Can I ask why you've ruled out conures?
Also, have you looked at Pionus or Poi's? They're usually regarded as more "hands off" but my pionus loves scratches, is very easy going and an over all pleasant bird. My conure Kiwi is the cuddliest bird I have ever had the joy of caring for.
I don't know much about HH parrots, as they're expensive and few and far between here in the states. But I've never known them to be "cuddly" birds, maybe there's just a lack of information though because they're so scarce as pets.
Eclectus parrots generally are "hands off" also. Mine hated hands, but he was a special case(was neglected). Some members have ekkies who will accept petting or cuddles but it greatly depends on the bird. I wouldn't be surprised if an ekkie went either way, cuddly or completely hands off.
Mini macaws that I've seen can be "cuddly" but they're also fire crackers. They're pair-bond birds, so they do tend to become "one person" and that subjects you to displacement aggression if you don't address it from a young age. (EX. Biting you because they can't bite the person/bird/thing that is upsetting them.)
I'm trying to think of another species to suggest, but it sounds to me like you want a conure.(But you don't).
Maybe a Caique..? They're generally playful, happy birds, but they also tend to have fire cracker personalities and can be difficult to read if you don't know what to look for..
Best of luck on your search. Don't give up on a species entirely, you'll never know what picks you.