This is my first post here, hello to all!
I'm a mechanic at a JD dealership and I purchased a 1130se this year. I have good luck with my machine, but like many of you, it would occationally slip in the lower gears (F or R).
From what I have seen at my location in central ND, Deere doesn't have anything for solutions.
After reading the info posted here I sealed up the gearcase underneath the engine. I used JD "combine sealant" (yes, that's what it's called). I used it since it matches the green paint and it costs less than $10. Once we finally got some snow I am happy to report that the slippage problem is gone.
Locally we have come up with another solution for the slippage problem.........there are two springs that actually press the rubber drive wheel into the steel wheel. The are located at the very bottom of transmission housing. Remove those two springs and take them to your local hardware store and match them up with replacement springs that have a larger wire diameter (they will be stiffer and will press the wheels together tighter), but are still the same length. To get the springs installed you may have to remove the engagement cable (I did) and re-adjust the length of the cable once you get the new springs on. The handle will be slightly stiffer, but not horrible. Total cost for this mod is less than $5.
Hope this helps!