Just to test things a bit. Start the engine with one plug wire unplugged and see what happens, then try it the other way around. I am guessing that the problem will point back to the original head.
Also, there Is a concern about your checking the flywheel key, if you didn't not put it back together with enough torque, then this could be a secondary problem.
Ok, here are some updates and more information on this issue.
1. The extended spec number requested is "PS-SV730-0034".
2. The backfiring and fire breathing behavior have stopped. I think something was obstructing flow in the muffler and that might have been causing some of my problems. There was lots of backfiring, fire blowing, and the exhaust was glowing red until a large backfire blew the lower half of the muffler and all the guts off and then I ran over them with the mower deck as I didn't know they had fallen off. There was a large explosive backfire just prior to this so I think this blew part of the muffler off. It hasn't backfired, blown fire, or had glowing exhaust parts since this time. I plan to replace the muffler if I get the other issues solved as I now have to wear earplugs to mow.
3. I have had other problems though. The intake valve rocker arms and push rods on both cylinders have given me similar issues. The first issue was with the right cylinder as you look at it from the front. The first problem was when the lock nut came loose allowing the pushrod to fall out of place. I tightened it up and used Loctite and set the lash to .006. The manual calls for .004-.006 and I figured setting it loose might be better on an air-cooled engine. This then pierced the pushrod right through the rocker arm. I replaced the pushrod, rocker arm, stud, lock nut, and pivot and applied Loctite. The same thing happened again after about 2 more mowings. I then replaced just the rocker arm and pushrod and set the lash to .006 once again. It lasted just about one mowing before putting the pushrod through the rocker arm once again. I then replaced the rocker arm and pushrod again and set the lash to .004. I have had no more problems with this cylinder and made it several mowings before I lost the other cylinder while mowing. Of course I was pushing through grass and the engine just bogged down and died. It flooded and was hard to restart and blew black smoke for a while once I had it running. I then putted up to where I could repair it and removed the valve cover for the right cylinder because that is where all the problems had been in the past. It looked fine so I put it back on and removed the left side. The lock nut on the intake valve had backed off and the pushrod fell out of place. I put it back together and set the lash to .004. I have mowed with it quite a bit without issues since then. I guess the lash likes to be set to .004 and not .006, at least on my mower. The engine just seems to run better overall like this but there are other problems.
4. The governor seems to be acting up. Sometimes it just revs wildly and sounds like it is going to take off. This is great when you are going through heavy grass but not when the unit is under no load. It sound like it wants to explode when it does this and it isn't under load.
5. I have been running Rotella T6 synthetic 5W40 based on suggestions from several people including lawn services who have great luck running this oil in all their air-cooled equipment. This is diesel rated and supposed to be better in high heat and pressure situations so I can't think of it being bad in an air-cooled engine like this, especially since there are no emissions sensors to foul. The insides of the valve covers are clean metal with no sludge or deposits.
6. I put the flywheel on to the specified torque in the manual with a torque wrench. I don't remember what this was but don't think the flywheel key is the issue in any of my problems.
7. I talked to a small engine repair guy and he doesn't much care for the Kohler Courage line of engines in general. He says he sees lots of problems with them and just considers them junk. He figures plastic gears in the governor are now going bad.
Conor