Considering everything you have done so far has not had any good effect on how it runs, you probably need to pull off some of the cooling shrouds and flywheel cover to see if mice have built a nest or a food cache in the cooling fins.
10 minutes run time on a blocked/partly blocked air duct is about right for a high heat lean out and possibly the onset of piston galling.

An exhaust valve with too little valve clearance can cause a cylinder to be "lost" or fade away when it gets hot.
Too little valve clearance on the exhaust valve can be caused by the above mice scenario if the high heat causes a valve seat to loosen/move. The high heat may also result in a rocker arm stud loosening/moving (causes too little clearance) in some models of Briggs OHV engines.
If you do not find signs of mice activity in your inspection, please post the engine Model Number and Type Numbers from the engine data decal/plate so we know exactly which Briggs you have.

I once worked on a rider that had the same problem. Even though the hoses looked OK, a cable tie had put enough pressure on the hose to restrict the flow of gas.

Remove the end of the hose and see how fast the tank empties by gravity.