I think you've figured it out. It's not medical, it's emotional. If your going to consider another bird, I would get another Hahns. Trinket has really blossomed having friends of his own species. He can't wait to get out of his cage to play with his buddies and he's plumb worn out at night and in his tent for nite nite so he can get up the next morning for another day of play.
I know how hurt you were and are by Maddies passing but I think you also love Max to pieces and have a big enough heart to give a home to another bird.
Ginger