The problem has been fixed. I replaced the ignition coil assembly that tested bad, and I spliced a severed kill wire that led to both coil packs.
When I lifted the engine cover to get to the coil packs, I saw that the kill wire was broken. Weird, right! No rodent marks or signs of heat-related damage. Since the engine has been hard to turn off ever since I bought the mower (new, ten years ago), I assume the factory guy didn't secure the kill wire properly, allowing it to move around and be chopped by the spinning flywheel the first time I used the mower. Who knows.
The engine kills as it should now.
I hope that the electrical tape I used to splice the kill wire isn't going to melt. I didn't know if I should use a plastic wire nut or electrical tape. Any thoughts?
Thanks for all of your help!!!!