Well, I feel dumb!
The old fellow who gave me the tractor said it was an LT350, and gave me an operator's manual for a 350.
Last night, I deemed it "time" to pull the transaxle, which is a fairly simple but fussy job.
By the time I'd gotten 10 years of oily grass mat stripped off everything, it became apparent that this was a John Deere 455 tractor.
It's not 32HP, it's 22, but it runs a 60" belly mower through knee high grass like it was 50HP.
The tranny is a Tuff Torq unit. I haven't yet uncovered any nomenclature on the transaxle that will show me a model number.
I THINK I noticed some wiggle in the F/R linkage D-shaft connection. One of the original respondents might be right -- this might just be a linkage problem.
But the tranny won't keep a load of oil... every gasket leaks. So it's time to get it out and fix everything in one pass.
Now that I actually know the model, any schematics floating around out there?
LLoyd