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cant shift into reverse

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I just acquired a new 7016 Simplicity 6-speed. I bought it for the snowplow attachment and got the tractor thrown in for free. ($250 for both)

I can't shift it into reverse gear. I can push the gearshift so it acts like it is engaging, but the gears grind and will not fully mesh. The tractor has had a lot of Tough, unLoving, lack of Care by people who don't know how to adjust the  shift and brake systems, so those are way, way out of adjustment. They also had someone do a $550 replacement of second gear in the transmission. I'm trying to diagnose the problem, and have found the transmission input shaft has more than 1/8 inch of end play. The two-sheave driven pulley slides in and out, and the nut on the shaft has been jammed to the end of the threads. This doesn't seem right. Shouldn't the nut lock the pulley against something? Would the excessive end play move the reverse gear out of the way? I am suspecting some  interior  or exterior shims or lock rings were left off the shaft when it was worked on. 

Does anyone have any ideas about this? I have looked at the  parts lists and service manual and can't find any spec for the end play.


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