Note taking app with a hand guard/hand recognition feature?
The general rule is to make sure you touch your device with your stylus first then rest your palm, it helps big time. Unfortunately, I have not seen an app with a dead area, but that means its not the "whole page". 

Samsung are the leaders for true stylus technology on android with their new Galaxy Note phone/tablet which may be the best choice for this kind of thing. 

May I ask what stylus you purchased? I have not seen any with pen-precise writing, it does not seem possible with the capacitive touch screen when you compare it to Samsung's stylus tech with pressure sensitivity and separate Wacom sensor.