Nick (mechanic) just called. He said your dealer SHOULD be able to look this issue up on Deere's 'system and find the resolution because he said that's what he did. I was wrong about one thing. He said he replaced an OIL TEMPERATURE SENSOR, not the coolant temp sensor as I stated earlier. He told me that this sensor works in conjuction with the fuel pump and therefore if it's screwed up, your pump will dump in the wrong amount of fuel, causing the smoke, etc. If your problem is the same as mine, this might fix you up. He told me I could call tomorrow morning when he's at the shop and get the part number. He mentioned again that a John Deere factory employee called him and talked to him personally and told him about this fix...and that if this didn't fix it, it would then involve looking at injectors, etc.
Side note...I've noticed in the phone business that you can be led astray when troubleshooting if you perceive the problem to be one thing when it's really something else. Someone might call me up and report that their phone is 'dead'...but in reality, they simply can't hear dial tone because their handset is bad, but the phone and line itself are fine. Your dealer might be explaining the problem to Deere incorrectly and therefore Deere is giving them bad advice. Know what I mean? Hard to say if that's what's going on, but when I had my problem, it only took my dealer a few days to find out what the problem was and fix it. Here's the kicker. I didn't even have to take the tractor in! I described the problem in detail on the phone and my mechanic found the solution without even looking at the tractor. It stayed in our garage the whole time. He came out one day and replaced the part.