When it starts surging pull the fuel line from the tank loose and see if you are getting good fuel flow from the tank. I have seen fuel lines collapse when they get hot.
I would remove the fuel cap and see if it smoothens out and if it does your vent hole could be plugged. That should also help get a better flow of fuel to the inline filter.
Try holding the governor arm still and see what it does. If the engine dies it is a fuel problem if it keeps running and smooths out it is a governor issue.