From what I learned about Patsy beforehand, it sounded like she could be a friendly and cooperative cat, but I could not be sure. The tree had very few limbs worthy of my trust for rope installation, so I chose one that was just opposite the trunk from Patsy's position. Fortunately, she was not frightened by my setup process. Indeed, she was curious about it and came over to the limb to play with the rope as I pulled it over.
By the time I started climbing up to her, Patsy had draped her belly over a branch in an uncomfortable-looking position with her back legs dangling freely. She stayed there and watched me as I approached. I climbed slowly and calmly while watching her for any signs of distress, but she remained perfectly calm. When I reached her, I held out my hand for her to sniff, and she did so with little reaction. I climbed up a little more and again reached out my hand to her. She let me touch her and pet her, and she quickly started purring and enjoying the attention.
I opened a can of food for her which she sniffed but, otherwise, found uninteresting. I put the food in the back of the carrier and held the carrier above my head and on the branch for her to walk inside. She sniffed the carrier entrance, looked inside with curiosity, and then walked in. Even though the food did not interest her, she calmly stayed inside during the several seconds it took me to pull the carrier off the branch and bring it down into position so that I could close the door.
I brought Patsy down and handed the carrier to her family. They walked her back home and released her there. She is doing just fine, as you would expect after such a short time in the tree, and the family is very happy to have her back with them again.