I just went through this exercise in the past couple of months for my 60" deck. My output shaft was severely wobbled out. The culprit was a loose split bushing which attaches the sheave.
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I saw only a couple of options at the time:
1. Buy used/rebuilt for $$$
2. Rebuild myself for much less money
I chose to rebuild the gearbox myself. Influencing factors in my decision were:
1. I have the time to rebuild properly due to being winter.
2. I am very wary of online replacement parts that are obviously underpriced.
3. And the biggest factor: I have partial ownership of a machine shop.
For your specific situation, you need to repair the output shaft. It likely underwent the same failure mode as mine. If you do not have easy access to a free/cheap machine shop, you may consider simply buying that output shaft new of JD. It is a $216 part, but you will have the comfort of knowing it will be rebuilt correctly and should last a good many many years.
If you choose to rebuild yourself, I also suggest replacing the shaft seals (2x) and the gear case o-rings (2x). You might have $250 total in the rebuilt if you buy that $216 part.
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Keep us updated in your decision making and show lots of pictures as you go.