Trouble with a Kohler CH 760-3051 engine

Hi,
 
I have a Kohler CH750 30 hp engine that is giving me issues.  The engine starts and runs great. However, after warming up the engine and opening the throttle wide open the engine starts surging or it may start to belch out lots of heavy grey smoke and appear to run on only one cylinder. I figured it needed new spark plugs and replaced them.  Engine still did the same thing.   I then thought there may be a head gasket issue as the engine oil had gas in it.  I replaced the oil and installed a new head gasket on the cylinder that happen to have a black oily coating on one side of the cylinder head.  After removing the head there was a gas/oil mix laying in the cylinder.  The valves, piston and cylinder walls were good.  I would have bet money that that was what was wrong.  However, after installing the head gasket the engine did the same thing.
I assumed that one of the coils was bad.  Replaced both to the new Kohler 2 wire kit and this did not fix the problem.  I also removed the flywheel to see if the key was sheared or damaged which it wasn't. I replaced the other head gaskets and checked the valves for leaks, no problem.  I removed the fuel shut off solenoid to test it - worked as it should.  No change on the operation.  Figured that maybe the engine was either starved for fuel or was overfueling.  Opened the gas cap on the tank, cleaned the fuel sump supply line and removed the filter to no avail.  When revving the engine it will sometimes burp up oil/gas solution and blow it out the air throat in a spray.  Almost like a backfire.  I am stumped as to what the issue is with this motor.  Any help would be greatly appreciated.   

Page 25:
 
chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://resources.kohler....24_690_06_EN.pdf    
 
(Copy, paste-search)
 
.

I checked the oil since yesterday and it is at the full level.  Removed the carb and blew out the orifices.  Reinstalled it and ran it.  Runs prefect at mid idle.  Speed it to high and it blows out grey smoke to choke you.  may even backfire a spew oil/gas out the air iinlet.  Seems to run on one cylinder only briefly.  I even thought that the cable from the battery may be an issue as it wore through to the frame.  put on a new one.  no change.  I am at the point of burning it.

Hi again.  Thanks for the feedback.  I inspected the muffler and it does not have a spark arrester.  No difference running with or without the muffler actually.
I checked the valves and they appear to be moving the same amount of travel on both cylinders.  The minimum lift clearance is slightly greater than what is specified in the shop manual for both intake and exhaust.   I did notice that the fuel pump diaphragm was leaking gas into the #2 cylinder which would explain the gas in the oil.  I replaced this with a new pump/valve cover thinking that this could be causing the running issue but there is no change. 
I made a video of the way the engine works and posted it on you tube so you can see what it is doing.  Here is the link:
 
 
Thanks

Yes I forgot to mention that the compression was 180 lbs on both sides.  Yes the pump is mechanical. 
I hope the link is showing as a image.  This site does not allow me to post a link to your tube. 

 

https://youtube.com/shorts/JjIBINIc4o0?feature=shared

Yes both are fouled.
 
In the video I slowed down the engine at the time it started to surge because it will continually do so at full RPM and the shop would be full of smoke.
 
Thanks

Thank you gentlemen for the information.