I have a Simplicity 6116, which is basically identical to your AC, and had similar carburation issues. I found that I also needed to rebuild the fuel pump, which is a $5 kit and an hours time at most. The old diaphragm was leaky and could not keep enough fuel pressure to fill the bowl at anything beyond 1st gear slow. The kits for carb and fuel pump are readily available on eBay, and are the same for most of the B/S twins of that era.
Also, if you download the parts manual from the Simplicity site, and look at the diagram of teh wiring loom, you will see where the two saftey switches are (#4) and that will steer you to their location on the tractor, one under the seat and one under the left footboard. The wires run through both of these from the ignition switch on their way to the solenoid. If you have no power coming into this path when in start position, nothing will get to the solenoid. If it is hot at one side of the saftey switch but not the other, the switch is bad or stuck. Just by-pass it with a piece of wire (for testing only), and determine which is in need of replacement.
Also, if you download the parts manual from the Simplicity site, and look at the diagram of teh wiring loom, you will see where the two saftey switches are (#4) and that will steer you to their location on the tractor, one under the seat and one under the left footboard. The wires run through both of these from the ignition switch on their way to the solenoid. If you have no power coming into this path when in start position, nothing will get to the solenoid. If it is hot at one side of the saftey switch but not the other, the switch is bad or stuck. Just by-pass it with a piece of wire (for testing only), and determine which is in need of replacement.