Need help with B&S Intek

I'll try to make a long story short.  John Deere zero turn mower with a B&S 24HP Intek OHV twin with 119 hours on it.
 
Wife mowed over a thick extension cord and it wrapped up in the blades and killed the motor.  After removing the cord the engine start but sounded pretty bad and smoked white.  Eventually it wouldn't even start unless the choke was full on and then it billowed white smoke.
 
I did a compression test and got about 55psi in each cylinder.  I could tell that both head gaskets were blown so I tore it down and replaced them.  Pistons, valves, etc all looked great.  Drained and refilled the oil.
 
On restart it fired up but blew black oil out the muffler.  Thinking the muffler may have got oil in when the engine died and mower was tilted up to remove the cord.  Removed the muffler and it starts but only stays running with the choke full on a belches white smoke.
 
Not sure where to go next.  I removed the intake and inspected and found no obvious damage.  Removed carb bowl and it's clean.
 
Any suggestions on where to go next?

Yes, head gaskets were blown but I'm basically having the same problem I had before the head gaskets were replaced.  I didn't check the flywheel key.  Good thought, however would it even start and run if the key was broken?