I only played 4-5 games iirc, so my 100% record sounds more impressive than it actually is! I also wouldn't be surprised if I played incorrectly, it sounds like I played the cat card abilities wrong so I suspect that I might have misplayed some other rule too.
As far as the actions, sorry my language wasn't too clear! I don't mean I was only using those actions, but most of the time I would prioritize flipping cat cards and once there were maybe four or more finches in the sky I would use the one action to return two at a time, which felt very efficient and still let me do other things without feeling like having birds flee to the sky was all that scary. I still definitely used the finch actions that move finches between garden spaces, but it just felt like those actions weren't nearly as important to winning as just keeping the cat cards managed and keeping on top of having enough birds in the garden. The main way I moved finches together was just having Ming move in a spiral pattern, having the finches she scatter move to the next space in the spiral and gradually get collected together.
For all but one of my games I did randomly select which card starts as a cat card, but for my third game I specifically experimented with having that one card as the starting cat card because it felt like it was kind of a safety net that made it so I wasn't too worried about what action I picked, so I wanted to see what it was like not having it available at the start of the game.