this^^
There is a lot of literature on the bean animal design. Naturally when increasing the flow through the tank the water level in the external box is going to rise. This will cause issues with the amount of water flowing through your "open" (what you call "secondary"). there are 3 ways to correct this and limit the water flowing through the open, ONE, is to open the gate valve to allow more water through the "full siphon" (what you call "primary") getting the water to trickle through the "open", TWO, raise the U bend higher thus allowing the water to trickle through the "open", there are a lot of things that you have to be concerned with when doing this, main one is not to raise it higher than the "emergency" stand pipe. THREE, adjust the flow through your tank and sump. Some people don't have the option to do this simply because it requires an adjustable return pump or the required plumbing to either divert water back to the sump or other components or restrict it with ball valves.
Looking at your videos, I personally think that the air bubbles are a result of a necessary flaw in the way the system was designed. The bean animal design never intended for the full siphon to have a hole on the top. I can only guess that the reason for this because the external overflow is so small and has little room to allow the water to build up in the external overflow to correctly create a full siphon.. Instead, it utilizes that hole to prevent water from overflowing onto the floor during start up and assist in eventually creating a full siphon. Normally this was fixed by terminating the full siphon (in the sump) slightly under the water so that the water level in the external overflow doesn't need to rise up too high to overcome the pressure created by the pocket of air trapped in the standpipe (again at start up). It's the best of both worlds the stand pipe is only 1/4-1/2" under the water and still allows for complete silence. Because that hole is there, it can never be a full siphon if it's occasionally drawing air. The water line in the external box needs to be high enough to prevent air from making its way into that hole or the U bend needs to be low enough to maintain a healthy distance between the hole and water line, not sure if you can lower it or not.
Another concern is to break up the rhythmic oscillation in the tank, It's great to show people that you can create this beautiful symphony with the pumps and create a perfect wave in the tank (I have a virtual outlet labeled "Wave" so that I can show it off to my non reefing buddies). I would strive more for of a random flow trying to keep that from happening. Looks like you figured out how to sync and anti sync, what I would suggest is get rid of the "constant" flow and trade it out with reefcrest, tidal or lagoon and anytime you use pulse or nutrient make one of the 2 on the right the master and simply make the other 2 anti sync slave to that one.