Well, I can only give general guidance since pianos can vary wildly even when you have two of the same make and model. It's not so much the key depth that's important as it is the point in the key depth where the escapement happens.
If the piano feels deep, I point my fingers down more from the knuckle. the metacarpal joint, and I stay closer to the keys and use a bit more weight from the arm. Just a touch more, nothing too drastic. When the keyboard is shallow I actually find a less pointed finger, almost a flatter hand attitude works a bit better, with the fingers pointed more out the way than down the way. I use a bit less weight otherwise it can feel like I'm hitting a hard surface because my finger travel will continue after the key has sounded. When it's a shallow touch I use less weight and feel more like I'm playing outside of the keyboard rather than inside it.
If the piano is a bit stiff, I tend to use a bit more finger action, but it's a downward - inward action, pulling the finger in towards the palm rather than a vertical motion, and then release from the palm so that the finger resets to the starting position without being pulled upwards.
Does that help?