19 HP, B&G Fuel Feed Problems

[CraftyRider]

I have a Sears 42 inch riding mower with a Briggs and Stratton 19 HP engine that runs great when I first start it up, but begins running progressively slower in a about a 10 minute time frame. I though I may have had a clogged fuel filter so I purchased a clear aftermarket model. As you can see from the picture the filter is 95% full of fuel before starting, but as time goes on the fuel level in the see thru filter empties to about 5%.

If I turn the ignition off it won’t start back as if I have a vapor lock, but removing the gas cap has no effect. After 30 minutes of colling down about 20% fuel builds back up into the filter and it will start again. I readjusted the carburetor air for as richer mix and it helped a little. I’ve checked the fuel lines on either side of the filter and they’re clear. The mower is about 10 years old and has not seen much use as I hire my yard to mown when I travel on my job. I can only conclude I need to rebuild the carburetor. Any advice would be much appreciated.