First off, put the engine upright on a test stand and see how it runs. If it will run properly "all day" on the test stand, then the problem's in the installation.

Vibration-induced fuel foaming is very, very common. That means that the engine's vibrations agitate the fuel in the tank so that air gets mixed into it. This effectively causes the engine to go lean.

Inverted running usually causes problems with idle and low-end acceleration, but throttle-down from full to mid should not cause the engine to quit. We'd look for another cause.

Since engine is cowled, we'd wonder how well it's being cooled. You need to make sure that the air flowing into the cowl actually flows THROUGH the fins of the cylinder. A large opening in the front and a large one to the rear don't insure airflow through the engine's cooling fins. You may need to make baffles to insure proper cooling airflow.