You CAN' T be sure a tree won' t get smaller as you go higher because they DO just that.

Your stand should be mounted to the tree so that the edge furthest away from the tree is significantly higher than the part contacting the tree--experience with it will help you to estimate how much.

As for slipping---most climbers have some sort of strap assembly--even bungee cords--that are used to secure your stand once you' re at the height you want.