Are you able to visit bird stores and listen to the birds and play with them? People tolerate different levels and pitches of noises, and so, since you specifically request a quiet bird, I would say that if you can visit the birds you are considering and listen to their calls that would be best. I don't think anyone else will be able to predict what you can actually tolerate. Also, I would give the same advice regarding the feather dust. If I could handle it, I would have a cockatiel, but I know I can not handle that particular dust, and I don't think anything except exposure to the dust will be able to predict whether or not you will be able to handle it. Cockatoos make even more dust than cockatiels. African Greys also produce a dust.
If you REALLY want a grey, look into them, but do a lot of research before you decide. I have not heard anyone describe a grey as particularly cuddly, but probably some are. They can imitate very loud noises if they hear them, but unless they pick up imitating something annoying, they make a lot of interesting noises but not necessarily unpleasant one. Their own flock calls are not that bad.
Quakers can become very aggressively cage territorial, or just plain aggressively unpredictable, or they can remain sweet throughout their lives. The ones who remain sweet are dearly loved. I have no idea how you might predict what a baby would develop into. Perhaps some quaker owners can give some insight.
Poicephalus can also become aggressive, but it is often a fear aggression or a hormonal aggression, or they can remain sweet. Again, I have no idea how to predict what any particular baby might become. I love my senegal, but she has already gone through one rough stage and I expect more. You could pet her for as long as you wanted. She never tires of that. She has a piercing contact call. I do not know any other way to describe it, although my son likens it to someone scratching fingernails on a chalk board. It really doesn't sound as bad as that to me, but he is younger so probably hears more pitches than I do. She will contact call if she wants me, but ignoring her and very consistent responses have lessened that a great deal. Honestly, for ME personally, I don't mind any of her noises, even her contact call. I wouldn't even have worried about trying to teach her to call less except for the fact that the contact call bothered my son. The rest of us here are not bothered by it. Senegals can be nippy, but training can also curtail that, although during hormonal swings or phobic stages you would probably experience getting some nips. Note that my senegal has given a lot of nips but never broken the skin or left any welts, but some pois do. Meyers and brown heads are supposed to generally be sweeter than senegals. I'm sure some if that varies from individual to individual, but, in general, meyers and brown heads are noted to be sweeter than senegals. Cape parrots, which are now sometimes called Uncape Parrots, Brown Necked Parrots, or other names, are supposed to be the sweetest of the pois, but they are very expensive. They are also noted to have the ability to talk nearly as well as African Greys. They are much larger, closer to the size of African Greys, but don't have the dust like greys have. The only problem I see with them is that there are not very many who have lived as pets long-term, so maybe there might not be enough information to know if they would become difficult or not.
Pionus are generally quiet and sweet. Maximillians are the largest and also noted for having exceptionally sweet personalities. I am sure other pionus are sweet, too, but the Maxi's are noted for being really sweet. Individuals do, on occasion, develop into loud birds, but this is the exception, not the rule. White caps, although the smallest, are generally considered to be the fiestiest of this group. They are not noted to be especially cuddly or playful, but they are supposed to learn to do what is wanted of them very easily, so I would think that if you interacted often they could come to like that.
I would think pyhurrah conures would fit your criteria better than the other conures, but I can't be certain. Suns and Jendays are very sweet in general and also quiet noisy. Look into crimson bellied conures if you can. They are supposed to be similar in personality to the suns in cuddliness but not as loud. Really, any of the pyhurrahs are quieter and noted to be cuddly. They DO go through nippy stages. It is part of it. I had a dusky conure years ago, and she was never loud and never mean. I have never personally known a dusky conure owner to report anything different of their dusky, but I have seen some described in the forums who are not sweet. Mine was sweet and cuddly and quiet, but she never spoke that first word.
The princess of wales is a very different bird and not popular in my area, but might be a great fit in a house full of budgies. I think sometimes it is easier on birds to socialize with others who are at least coming from a similar continent. They seem to instinctively understand one another.
To me, cockatoo calls are unbearable. If you want a cockatoo, do visit with them often to be certain you can tolerate the dust and the sounds.
Linnies and lories are out because you specifically requested a more solid type pooh. I have had both, and was not bothered by the pooh of either, but that was me. The pooh IS more liquid than that of other parrots. Lory pooh is more liquid than linnie pooh.
I have to second the advice to look into an older bird. At least consider it. Of course, MANY rehomed birds are rehomed because they have issues, but if you are fortunate enough to find one that is being rehomed for another reason, such as a change in the owners circumstances or the owner's death, you might find one with a great personality that just fits you. You will have a great chance of knowing what you are getting, because the bird will be settled. They do change a great deal from the time when they are just weaned until they are full adults.
Good luck in your decision. This is a fun time.