Just wanted to update this thread and thank TimberHole for all of his advice. My Dad and I spent last week (~6 days of work and 10 hour days) rebuilding the engine in the JD1050. At certain times, we weren't sure if the thing would go back together and we made one major screw up that we were able to fix relatively fast. But I can say now that the tractor runs and purrs like a kitten. Everything seems great...
We started the first few days by pulling the other two sleeves / pistons and cleaning them up. There was some scuffing on the pistons but nothing too major. The oil control rings on all three pistons broke when they came out though. We thought this was a result of an overheating event or water in the oil in the past.
After spending a lot of time cleaning and preparing all of the new parts, we got everything back together Friday night down to the last bolt tightened and started to fill the radiator with water. Well, we heard lots of water dripping and it was coming from the head gasket area. We were completely devastated. These JD1050 tractors have two head gaskets depending on a serial number break and I had called a JD dealer with my S/N and was told to order the early head gasket based on my S/N. When we put it on, we noticed that the fire rings on the head gasket laid on top of the raised edge of the sleeve that sits above the block surface and not around it. We figured that this was the problem and fortunately, I had the later S/N head gasket in stock that I had previously ordered thinking it was the right one.
Well, after dinner on Friday night, we pulled the head again and replaced the head gasket with the correct one. It was a marathon but I think we pulled the head and got it back together in less than two hours which is pretty good, in my humble opinion.
It wasn't until Sunday that we were able to fire her up but after bleeding the fuel lines, she fired right up and ran beautifully. Hardly any smoke at all! I'm running JD break-in oil in her and the proper JD Cool-Guard II coolant now. I'm hoping for years more service from this tractor.
I don't have many pictures, so sorry about that. The next job is to sort out the hydraulic system which I believe is getting air into it from a leaking SCV, cylinders and old hoses.