Many years ago someone posted the GM part number for its steering-gear self-leveling grease. The grade was 00.
That grade of grease will self-level at most ambient temperatures, protecting all surfaces.
If you are putting less that 10,000 miles a year on a vehicle that mostly drives on highways, you could most likely use any grease-oil concoction and never notice a problem.
Too thin a grease-oil concoction might more readily leak out.
The John Deere product is NLGI 0 (thinner than the GM product), but it will work just fine.