Very good observation about the filter.
Think about how the fuel pump works.
There is a chamber with 2 poppet valves (in and out)below it is a diaphragm and below the diaphragm is a spring and the lump arm.
When the cam rotates the lobe pushes the arm up which pulls the diaphragm down and compressing the spring. This pulls gas into the chamber. When the cam lobe moves by, the spring pushes the diaphragm up forcing the gas out to the carb.
If the carb is full and the float valve is closed there is no where for the gas to go so the diaphragm stays down. The spring keeps the fuel pressure up waiting for the carb to need some.
The pump can't pump when the engine isn't running.
The filter is above the level of the fuel tank so gas can't run into the filter by gravity.
So the only way the filter can fill up is if the diaphragm was holding the spring down when it stopped and something released the the back pressure so the gas could flow as the diaphragm came up.
Possible answers:
Outlet side
Float valve stuck closed and then released
Vapor lock
Inlet side
Blocked fuel line
blocked tank air vent
If there is a blockage on the inlet side a vacuum will form in the pump when it can't draw in gas. As the blockage slowly leaks by or air slowly leaks into the tank the vacuum will draw the gas into the tank and will be pushed through until the pressure is equalized.
1. Try driving it with the gas cap off (I know you changed the cap)
2. Wrap wet rags around the gas line and filter after the pump.
3. Wrap wet rags just around the float bowl and fuel inlet. Do you have a heat spacer under the carb?
4. When the problem happens and the filter shows little gas, tap the float bowl sharply a couple times with a screwdriver handle or plastic hammer.