I just finished another pond with this same design. It is a small 1/3 acre pond. It has a watershed around 3 acres. So two 4 inch pipes should be enough. I just finished it mid September. So here are some pictures of that install with a little description of what I did:
I used two 4 inch sdr 35 pipes for the primary drain with a 2 inch vent. I used a 6 inch sock pipe to allow the water level inside the dam up to the 2 inch vent. All this is just in front of the core.
Here you can see where the sock pipe resurfaces on the slope of the dam.
I covered the sock pipe in #2 gravel.
I'm at full pool and my grass is coming up, I haven't had enough rain to confirm if it will go into syphon. My dam is 16 inches higher than the full water mark and my emergency spillway is 6 inches lower than the dam.