I realize how difficult it must be to have to find a home for a beloved parrot because of unexpected circumstances or life changes. I respect anyone who makes the right, often heartbreaking decision in the bird's best interest instead of their own.
Three of my birds came to live with me because the owners no longer had a place in their homes for them. I keep hearing a rehoming fee insures a loving permanent home for your parrot. I understand that it may make you feel good, and I agree, it's far better than giving the bird away, but accepting a predetermined dollar amount from a stranger doesn't tell you anything about your bird's future home or owner. Also please keep in mind, after you find that home, the new owner usually has to make an immediate cage and accessory purchase and a vet visit. In some cases the first owner wants the new owner to refund every penny they spent on the bird before they decided he or she was no longer a good fit. Not accusing, but it is true in a lot of cases.
I would be overjoyed if my Cockatoo and my Quaker's former owners would have wanted to keep up with their birds after they came to live with me. I have no desire to be friends with their previous owners so I post photos and updates for each of my birds on my FB page. They could check on their birds without contacting me if they chose to. I am so proud of my birds' progress, I never miss an opportunity to brag.

My birds' former owner made the transition so much more difficult than it had to be. She gave me no information about their diet, their health, their favorite toys, nothing. The birds told me everything I need to know. Well, almost, they still have their secrets. On the last day my poor birds spent with their first mom, she threw a screaming, hysterical hissy fit and unbelievably grabbed the cockatoo, bear hugged him, and slammed him into my son's chest, upside down, while she ran out of her house having an award winning tantrum. I'm not sure who the performance was for, she contacted me to take the birds. She didn't need the money for an organ transplant, she gave the cockatoo up of her own free will, because he is loud, imagine that! She demanded I also take the Quaker because she didn't like him. I adore him. She was not under duress to sell the bird, it was her decision. I had no problem with her histrionics, the birds did. She caused them so much undue trauma. Some days my bird room is like teaching an anger management class for birds. I don't blame them, I'd be angry too. The point I'm trying to make is I could have payed far less for the bird of my choice and brought home a just weaned baby, used my training abilities and funds to give the baby a great home. I think it's wonderful that people are able to do that, if it's right for them. Baby birds need good homes too, it can be such a rewarding experience and the birds lucky enough to get the right owners the first time, don't become rescues.
I'm not a rescue, I've never shopped for a free bird. I'm very picky about the next bird that needs a forever home. I think if you are looking for your birds next owner, you have every right to be picky. If the potential owner isn't willing to discuss your bird's future with you in a reasonable way, it would make me very suspicious. It wasn't my intention to rant, but to offer a view from the other side as well. There are excellent homes to be had for your feathered friends if you look for them, just like there are excellent original owners looking for the best opportunity for the bird. I wish you and your bird the best possible outcome.