This has me leaning towards a coil breaking down when hot. The spray bottle shooting a stream of water on the exhaust pipe works well. If the water immediately burns off, the cylinder is producing power. If the water is slow to burn off, that is a cylinder not producing power.
Firmly bolted V-twin engines do not rock or give an obvious indication when one cylinder drops out, it just loses power and will stall, especially if the deck is engaged.
The second suspect is there is a floating chunk of debris or a dead bug that is intermittently blocking the fuel line spigot/ pickup in the fuel tank.