the CORRECT oil is some engineers opinion, they specify all the aforementioned oils with the same result, the transmission works. although I agree that some form of gear specific oil should be used as there is extreme pressure additives to deal with the high shear loads encountered in a gear box. However that doesn't change the fact some engineer has specified any of the above oils at one time or another. Using a synthetic will allow a lighter oil to be used due to the superior lubricating qualities giving better efficiency. But in this application whatever benefits gained with synthetic is probably moot, as there is so very little stress generated with these engines, and if you are after fuel economy you are driving the wrong vehicle. Personally I like synthetic. (yet another opinion) So to answer the original question, if you want to use synthetic and aren't concerned about the extra cost, go ahead, the only disadvantage is the above mentioned extra cost, in all other respects it is a superior product.
