The cuddliest birds I have ever owned have been the GCC. They scoot around all over me and snuggle right into my neck and would be happy to sleep there all day long. If they can find a way, they will be in your shirt or hair or in your pockets. Too close is not in the GCC vocabulary. They would try to be under your skin if they could LOL Even at about 6 years old Kermit was still a huge snuggle bug.
My Galah was very cuddly as well and so were my lorikeets. All would love snuggles and head scratches. When my Galah felt like it, he would snuggle right into me or burrow into my clothes.
I recommend GCC for something thats reliably cuddly. Even my male who is very very reserved will not pass up a snuggle. My GCC will let me pick them up over their wings without argument and Colada allows me to turn her on her back. They both roll over on my chest or lap for belly scratches/tickles. Colada frequently falls asleep on her back on my shoulder snuggled into my neck (and falls off quite often LOL). I have owned three so far and not one has failed to be cuddly. Beware though, anything cuddly will also be "nippy". It kind of comes with the territory I find. It could be as simple as them grooming you too hard when they are in love snuggle mode. Or it could be that you aren't snuggling/preening them exactly where/when/how they want. Or sometimes they get riled up and want to wrestle. Human skin isn't protected by feathers so what they may think is acceptable often isnt.