Does the machine run smoothly, or does it feel like it has a miss? Does it have reasonable power? Will it push a bucket full of dirt, or at least spin the wheels if it cannot?
If cracking the injector lines didn't produce any result, anywhere, you have consistently established that you weren't opening the line enough to do anything. That is, if you couldn't tell any change in any of the three cylinders, it's obvious that test wasn't changing anything sufficiently to find a dead cylinder. Your tractor doesn't sound like there is a dead cylinder, it sounds like you may be leaking fuel into the crankcase.
I'm assuming you have changed the oil after draining it. Has the oil level risen since then? If so, then there is something leaking into the crankcase. That will need to be addressed, one way or another. If the shutoff valve doesn't work, that won't cause the problem itself, but will make servicing the system obnoxious.
If the tractor were mine, and the oil level hasn't changed for a few days, here is what I would do: First, I would check to see if the shutoff valve was repairable. If not, I'd order one from Hoye or LMTC so they could ship it to me this afternoon or tomorrow morning. Then, I would replace the air filter. If the plastic cover you're talking about is something non-factory, I would remove it.
Next I would put whatever is the heaviest implement I had (Like a disk or box blade or something) and work the tractor as hard as I could. It's possible the rings have sat for a long time, and are just stuck. I'd do that for 15 minutes or so, then check to verify the oil level wasn't changing. I'd try to work the tractor hard for at least an hour, enough to get everything good and hot and loaded. That will probably loosen anything up that will.
Then, I would reassess your situation. Does it still smoke? When, and under what conditions? How much? Has the oil level changed any? If the smoke went away and the oil level didn't change, I would keep the tractor stored with the fuel turned off, and use it. If the smoke stayed but was manageable, I'd keep using it. If the oil level changed in less than an hour's use, I would start planning to diagnose it more thoroughly and start budgeting for my repairs.