Are you getting a good flow of fuel out of the fuel line leading to the carburetor? How did you clean the carb? Was it fully disassembled? What did you set the float at?
What model, spec, and code number is XXXXX engine?
Which screw are you referring to? Was it on top of on the bottom of the carburetor?
The governor doesn't affect timing at all, it affect only the position of the throttle in response to changing loads.
The numbers I'm referring to will be on a tag on the engine shroud. There will be something like H70-35782A followed by a code or serial number. That will tell me which of many versions of 7hp you have.
Did you clean the small holes in the bowl nut really well? Including the one by the threads that's really hard to see? Did you probe them with soft tag wire or compressed air? It really sounds like a plugged main jet.
My bet is that's an H70-130210D. If that's the one, there will be a main (high speed) adjustment screw on the bottom, an idle mixture screw on the side, and an idle crack screw on top that prevents the throttle plate from fully closing.
Let's go through an adjustment procedure as well after you verify the jet.
Start with the main screw underneath the carburetor set at 1-1/2 turns from gently seated. Do not overtighten. Start with the idle screw on the side at 1 turn.Start the engine and let it warm up to operating temperature, usually about 3-5 minutes.Move the throttle to full speed. Start with the main screw and turn it in 1/8 turn at a time, give the engine a few moments to adjust to the new mixture at each stop, and note the position of the screw when the engine starts to sputter.Now turn it out in 1/8 turns just like before and fine the other point at which the engine starts to sputter.Set it halfway between the two points.Now bring the throttle down to idle and do the same thing with the idle screw.If further adjustment is required, the main adjustment should be made with a load on the engine. Engage the auger. If the engine stops or hesitates, turn the main mixture adjusting screw out 1/8 turn at a time, testing each setting, until it engages properly.If the engine smokes excessively, turn the main adjusting screw in 1/8 turn at a time, testing each setting under load, until this condition is corrected.After the main mixture is set, move the throttle to the idle position. If the engine does not idle smoothly, turn the idle mixture screw 1/8 turn either in or out until it engine idles smoothly.
Did you clean off the carbon in the head and inspect the valves for proper seating? Do you have a compression gauge to take a cylinder reading by any chance?
Let me know and we'll continue.