Craftsman Lawn Tractor Won't Start?

I have a Craftsman DYS-4500 (917.276906) lawn tractor with a 26HP twin cylinder Kohler engine that won't start. It was running fine up until about a week ago. While I was cutting the grass it just stopped. No loud noises, no metal clanging or anything like that. There was a bit of smoke, like burning oil, but that's not uncommon with this mower.

When I turn the key the engine spins, but there's no indication of any kind if ignition.
At first it seemed like it was just not getting gas. I checked the tank, which was full. The fuel filter seems fine; I replaced that last year. I replaced the fuel pump, which is a disk slightly smaller than a hockey puck. It works off a vacuum line from one of the valve covers. I also disconnected the outlet side and cranked the engine and got a pretty decent flow of fuel. So it seems gas is fine.

I pulled one of the plugs to check for spark. I left the plug resting against the engine, cranked it and got spark. So far it seems like I have gas and spark.

I sprayed some starter fluid into the engine, but even that didn't do anything. Not even a hint of wanting to fire.

I cleaned the air filter and even tried with it off - nothing.

So, it seems I have fuel, air and spark, but no firing.