Hey why to make it soooo sophisticated and poor?
Air valve cannot be designed with 2 stiff elements - it will never work.
Make the air your friend but not the enemy. Use old good rubber (silicone) "flake" instead. Especially when you have such small design.
Take a look on the picture.
Here you have black element which is rubber or silicone. It's sticked on one side. When air goes from the pipe (goes up) then rubber is slack so the air can flow. When you suck then rubber seals the pipe.
You can find such solution in for example bike pumps, inflatable matterss pumps also gas masks and so on. It's pretty fine for low pressure.
Of course ball valves are also widely use but then such device has to have "rubber" ball nest so ball lies on the rubber ring to seal it. There has to be a spring to tight the ball to the ring. Without such spring turning the device upside down would cause the valve would not work at all.
Ball solutions are intended to higher pressure.
Please note the spring which tights a ball creates kinda threshold on the pressure level which means that pressure has to exceed a spring force to reduce a pressure. This doesn't occure in rubber valve.
I don't know what device you are trying to prototype but I'm pretty sure a rubber valve will be just fine.
Please also note that sealing surface is very low in ball valve solution but in rubber valve it can be almost unlimited so it can seal quite well even when the surface is not perfect.