I agree with Alex on the one turn lunar approach. I've never had much success with hanging big cup lunar starts, and have had even less luck with one turning from that position. Learn to control your airplane so the small cup lands facing you every time. If you can start with the ken parallel to your shoulder angle, rotate with your fingers while the airplane is extending, and pull when the cups are perpendicular to your shoulder angle, you will find that you can turn everything and the ken will operate in a predictable manner.
Now to catching that bad boy! I have found that a lot of my focus goes into making contact with the big cup, yes, but then also "soft catching" it by rotating my hand back to match the speed it's coming in with. This prevents the ken from starting to slide off the tama immediately. If you try to make the middle of your cup the bullseye, and you're trying to hit it with the hole, that's a good reference point.
For lunar flips, practice knowing your forward and back limits to where you can hold a lunar on your kendama. Place the ken in a lunar. Rotate forward until it falls off, and backward until it slips off. If you go down with your knees, and take the ken to a more forward position, then as you come up with your knees, it will allow you more time to apply force on the ken.
Set up the camera, and go for it. You might be surprised at how many attempts you can get in what feels like a forever time frame. I used to think it would take hours to get a lunar flip. Turns out I only had to try for 4 minutes. This isn't training advice, it's more confidence talk. You can do this trick, and in a lot less time than you think you can. Good luck!
