1. It works fine after it has been sitting for awhile. Maybe the first 10mins or so are fantastic. Their is a point when the
Engine runs right its a intermittent problem these can be a pain to figure out
Sounds like you have a fuel delivery problem to me I come to this conclusion after sifting through all your comments, here is my thoughts.
You say it runs better when the Engine is cold, when the Engine is hot and you have a fuel starvation problem they Engine will run hot and any carbon inside will make the Engine continue to run even with the ignition switch turned off.
5. If I turn the idle up too high, the kill switch won't work. Next time that happens turn on the choke see if Engine will die, what turning on the choke will do is add more gas and cool the combustion chamber to the point were the air/fuel will not self ignite.
If it was mine I would go through the entire fuel system from the gas cap to the car ensure the inside of the whole system is clean and free flowing, make sure all the fuel lines are routed right, make sure the pulse tube for the fuel pump is still hooked up, make sure the bypass valve is installed correctly and working right.
If you see any fuel dripping out the lines on the carb then their is a problem with the fuel level or the float valve sealing.
How are the Engine mounts if they are all broke they can allow the Engine to shake more than normal this can upset the float in the carb, shake up a water bottle look at the bubbles you created same thing inside a carb you can actually make gas foam in a carb from excess vibration, if this is a bot bore Engine it probably vibrates more than stock, the extra HP and torque are probably stressing out the old dry rot rubber Engine mounts.
A exhaust leak can suck air into the Engine and cause it to run lean this needs fixed ASAP
Take a bunch of detail pictures of your machine and post so we can see what were working with many of these machines has been greatly molested over the years by previous owners.