Power valve is operating normally.

Engine sputters and wants to shut down at higher rpms.

No spark arrestor in silencer

Give your fuel the "jar" test.

A sputter at high RPM could be jetting or electrical.

I cannot remember when I saw a LT500 with the air box lid removed and a 370 main jet be so rich that it makes the engine miss-fire.

Install a new spark plug.

Disconnect the kill switch.

If that does not help, inspect the inside of the silencer for broken bits that would add restriction to exhaust flow.  An over restricted pipe will make engine act like the carburetor is rich.

If the silencer is ok, replace the main jet with a 350 and see if the engine runs any better.

If the 350 main jet does not help any, it is time to start checking ignition components.