Good news on the tranny coming along in a promising way!
I'm thinking you got your description of the other work a little twisted up. The piece you got in and greased from the port on the side of the bell is the carrier for the throwout bearing. Tht carier is basically a bushing in that holds the bearing and slides it over your driveshaft to move the bearing into and out of the clutch fingers.
The bad news is that there is no easy way to deal with the pilot bushing, which is held by a tension fit into the rear end of the motor's crankshaft. It's only purpose in this weary old world is to support and center the front end of the shaft between the motor and the front of the transmission. It's a frightfully simple thing, nothing more than a bushing to the eye, but is made of what they call Oilite, which is a bronze-type alloy made in a way that it has some lubricative properties. And there's really not much to wear on it, but it picks up crud and gets sticky (from picking up dust from the field or fine particles from the clutch, either of which is only made worse by any oil that finds it's way from the motor or creeping forward on the shaft from a leak at the front of the transmission).
The only way to get to it is to split the tractor between the motor and the torque tube, and remove at least the clutch to get it out with a slide hammer fitted with an internal puller jaw, and probably the flywheel (a minor consideration once you're that far into it) to do a good job of driving the new one in.
As I said, sometimes it's just crud in or around the bushing, and some folks have gotten away with just splitting, then cleaning it up and all around it, fixing any leaks that might have contributed to the problem as they go along, and clapping it back together without actually changing out the bushing. I'm happy for their success, but it's a lot of work (not ugly, just a lot of set-up and wrenching) for a small part to leave it in place when with another fifteen minutes and the price of the part, it could be replaced.
Before flying into it (or getting thoroughly disgusted and cutting up the tractor!), you might be able to capitalize on the good news on the transmission. Good new oil in the transmission might provide enough friction to stop the input shaft or at least least slow it down to minimize the problem. You don't say where you are on the planet (too far north and this might not be a viable option if you need to run the tractor in the winter), but a lot of folks have had success in minimizing the problems created by a marginal pilot bushing by putting a stiffer oil (like 140, or a multiweight with 140 as the higher number) in the transmission. If it behaves better just with new oil, and your winter climate isn't too severe, you might want to consider trying the heavier oil before deciding to split the tractor.
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Today's Featured Article - Identifying Tractor Noises - by Curtis Von Fange. Listening To Your Tractor : Part 3 - In this series we are continuing to learn the fine art of listening to our tractor in hopes of keeping it running longer. One particularly important facet is to hear and identify the particular noises that our
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