I take it that the engine does not even TRY to start, but just spins when the starter is engaged. You need to make the test that mownie suggested. There are probably more safety interlocks than just the seat switch, and one of them could be "shorting" out the system. There is likely one on the clutch/brake pedal, and another on the PTO lever (the one that engages the blades), and one on the shift mechanism (to prevent starting if the transmission is in gear.) Testing these will require a multimeter. There is also a ground wire from the engine to the frame; typically on Husqvarna/AYP/Electrolux/Roper machines, it is a rather small black wire that is attached to the underside of the tractor frame just below the engine and inside the right front wheel. You've likely got a bad magneto or (more likely) either an electrical short caused by chafed insulation, corrosion, or loose connection, or a malfunctioning safety interlock switch. This all based on your being certain that there is no spark at the plug.

I moved an S&S that size last fall to a different bed, no problem. It looks fine this year. I also moved a Queen of the Seas this spring (not quite fully unfurled) that was a little easier. And a large Journey's End, Paradigm, and Inniswood a couple years ago, just a few feet, and they were so much easier. Water the plant a day or two before. Dig your hole where the plant is being moved. If they're that close, go ahead and dig out the soil between the new hole and the existing plant. Just use a shovel to slice a line about where the leaf drip line is. Since S&S has such big floppy leaves, you can probably be okay going a foot in under the leaves. Remove some of the soil until you see roots. Then dig your shovel deeper and start lifting up each side of the root ball, all the way around. Angle your shovel mostly horizontal and go deeper the next time around. Eventually you'll get directly under the center of the plant and shovel through the last piece of connected soil. Dig out the rest of the soil in the trench between holes. Use your hands to wipe away some extra soil if you want, so it weighs less. Then I just manhandle the root ball across the trench to the new hole, often using the shovel as a lever. Position the plant, fill in the soil, and water. S&S didn't matter, since it was late in the fall. QotS finished unfurling this spring and looks great. Inniswood looked perfectly happy even in mid summer. Journey's End and Paradigm were in more sun, it was full summer, and I forgot to water as much. They had some outer leaves yellow and dry but were also okay.

I have a volume control lever handle, the Classic series. Is it possible that the handle isn't screwed in all the way? I've never had a problem with the lever changing position on its own, but I have found the handle connection to work its way loose, especially after I clean it. Looking at the exploded parts list for the Kensington volume control, it appears to have a 2mm screw that performs the same function as the handle connection for the Classic volume control. There should be a small hole that takes a 2mm Allen wrench to tighten the lever handle. Here is a link that might be useful: Kensington volume control exploded parts diagram

Are you sure this has a neutral safety switch? Likely what you are seeing is the switch that tells the tractor that it is in reverse for the mow/ no mow in reverse feature. If these are typical AYP circuits, the brake switch has to be engaged and the PTO disengaged in order for the switch to activate the solenoid. The 4 pole interlocks typically have 2 circuits- one NC and one NO. These are usually dependable,(like that phrase) and grounds and solenoids rate higher on the list for failure. I can look closer when time allows if this doesn't make sense.