Good to know, but that would make you a fairly rare bird considering that the average is may have heard, but little more! So, congrats on your knowledge base and welcome to the rare bird society!
As a World Wide Group, the Humane Society targets mostly Dogs and Cats as their base. The next part is Farm Animals, commonly manuals. Nothing against them, only pointing to their acknowledged main involvements. To that end, when Parrots come into their 'system' they move them quickly to a Specialist in which they have a working relationship. In other words, in and out very quickly! So, you can provide your name, but what comes in, is what your will get, rarely a question much beyond are you interested. Once again, not part of their system, so quickly move them to a Specialist!
Most Avian Vets in your area are going to have either a working relationship or knowledge of Adopting and/or Rehoming individuals in their area. So, ask your Vet as part of your next visit. If you have a Parrot Club in your area, JOIN! They will also be a good source since most of those individuals are also members. Once again, JOIN! Parrot Fairs in your area are either attended by or individuals at the Fairs can place you in contact with them. With care, check the INTERNET for Adopting / Rehoming Individuals in your area. Since, you have a relationship with good Pet Stores, remember that many of their adult Parrots are likely there for Rehoming!
We take in end of life Amazons. The majority come to us without our selection, with the exception of their being an Amazon. So, I am not really into any concern regarding whether the Amazon is 'right' for me. Since, we are only Amazons, I do understand being species specific, but beyond that...
First, ask yourself if you are Species Specific? The next, are you sub-species specific? This will give you a base regarding your discussions with Adopting / Rehoming individuals, since the good ones will be more interested in place a Parrot with a home that is Species Specific and have a history with that parrot family. If you are interested in a Species that is outside of your history, this group is not as likely to see you as a good home. The failure rate goes near vertical when there is limited to no history with that parrot family.
So, at this point you should have a base in place and should be able to find a source that has a couple or more of what you are looking and that you have a history of caring for.
Letting the Parrot Select You: Well, it is nearly that easy, you only need to be very open to that happening.