bth,
This seems to be a common problem. Your answer is in the first 2 paragraphs in the Service Transmission section of your manual. It is located in the section before the subsection titled Checking Front Axle Oil Level.
The recommended oil is Hy-Gard, either standard or Low Viscosity depending on the expected air temperature.
This was confusing for me as well for my JD 4310. The wording in the 4310 manual is the same. The reference to the recommended oil means the oil specified at the beginning of the Service Transmission section.
Jeff