Jim, thanks for the advice. After consulting a few people and doing some more reading, it seems to me that it could be 1 of 2 things:
1) shorted electronic device
2) poorly grounded engine component.
I am going to check all of the grounding wires on the tractor, clean them, sand them if needed, and reattach them. I would actually like to use those metal loops that you see on the terminal wires, maybe bolt them to the frame (there are plenty of holes all over it).
However, when it comes to the ignition switch, I have decided to install a push button for the starter. What I plan to do is to have a switch for the ground on the coil, then the button to engage the starter. They will have those ostentatious plastic covers that need to be lifted out of the way as though for the detonator on a bomb (once I get going with a project I begin to over-think and indulge in ways that are a bit immature, but hey...)
While I'm at it I am going to add another switch for the light, which I plan to mount on the hood (the stock lighting setup has been removed, I will also be removing the headlight bezels, and fabricating a new grill from some form of perforated metal).
The end result will be something vaguely shameful, but probably very good at removing snow at 4am, when my neighbors are sleeping.