If I'm reading you right, your input shaft will turn slowly and slightly after giving it time to stop after depressing the clutch pedal. It doesn't do so if you've got the PTO engaged. That suggests that the very little resistance of the PTO is enough to stop things for a "noiseless" shift (back to that in a minute). Since you don't know what's in the tranny for oil now, I'd suggest draining and refilling it with 90 or 85-90 as a starting/reference point, and see how it acts. If it's still noisy and balky, try going lighter, like to 75. My neck's out because I'm suggesting that a lighter/thinner lube might be enough lighter than what's spun up by the input gears might settle down sooner (while in neutral) might not be heavy enough to turn the drive gears. I could be all washed up in that thinking, in that it could be that thinner oils can be thrown more easily in there, and do more to turn the drive gears, making the grind you hear.
Bottom line, I'd say fill it with 90 or 85-90 as a reference point. Use your judgment after the results from that, and move to thicker or thinner lube and see which way reduces the noise.
That said, and to echo JimN, it isn't going to go away entirely. These are closely-meshed but straight cut, flat-top gears. Even when your input shaft spins to a stop, It's very likely that you will NOT have a tooth lined directly up to a notch for it to slip right into gear. Which will require letting up on the clutch pedal a little to spin the input shaft enough to mesh the gears, which WILL create a grind. It's the nature of the beast.
Not sure why your other tractor doesn't act the same. Could be that it's been jammed into gear with the grinding enough and for so long over the years that the ends of the gears have a bevel that meshes more smoothly. But I'll bet that it's a difference in the viscosity of the lubricant.
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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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