Well, to eliminate this as a problem, try cleaning out the fuel tank cap vent. The cap vent being stopped up (or partly so) can cause symptoms like this, especially if you begin mowing with the tank completely full. A good way to check this would be to run the tractor long enough for it to stall and die, then remove and retighten the tank cap. If the cap vent is clogged, loosening the cap will break the vacuum that develops when fuel is burned. Because you notice a difference between full throttle operation and 3/4 throttle operation, I would say your cap is not completely clogged, but very near clogged. Anyhow, this is cheap and easy to try.

Sounds like your not getting any power to the fuel pump, I would take the fuel hose from the fuel pump to the carb and disconnect it from the fuel pump and leave it connected to the carb then feel the hose full of gas and see if it runs.

On your solenoid there are 2 small terminals . 1 will have a ground presents if all the safety switches are online and the other 12V when the key switch is activated purple I think. If you have both- maybe you have a bad solenoid. This is old enough to where corrosion at the ignition, fuse block and brake switch connectors could be present. If you can safely jump across the 2 large terminals and it cranks, that would satisfy that side of the starting system- that the engine is crankable and the starter, battery and main grounds are good.

So I took the carburetor off, took it apart and sprayed every orifice down with carb/choke cleaner and then used an air compressor to spray out everything. Re-assembled it and viola! fuel flow. Now my problem is too much fuel flow. It fills up the carburetor and overflows into the air cleaner. If you shut off the fuel at the line, it will start and if you let it burn up all the excess gas and then turn the fuel line back on, it will keep running but very rough and lots of smoke and eventually floods out. So what is causing the extra fuel flow now. I checked the float and it moves freely.