If you can get the 803D for your self imposed spending limit of $7K, and you like neutral sound, go for it. Your P10 is rated 300WPC into 4 ohms and 40A per channel short duration peak. My guess is that it will output close to 400WPC into 3 ohms. Even if the 803D dips down to 3 ohms at low bass frequencies (I would say unlikely) the P10 will still have enough power on hand to control the speakers. That being said, you still need to be careful in the beginning, to make sure you don't push the amp anywhere near its clipping point or you risk burning out the diamond tweeter.
The Paradigm S8 is also a good choice but I think the 803S/803D are of higher quality overall.